Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
475 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 475 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13091375 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D9×#737 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C9×#4207 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D3×#4207 | — | 3 | 1 | no | maximal |
| 5 | D9×C3⋊D9 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | D9×AGL(1,ℤ/9) | — | 3 | 2 | no | maximal |
| 7 | D9×(C3⋊D3)⋊C3 | — | 3 | 1 | no | maximal |
| 8 | C3×D92 | — | 3 | 1 | no | maximal |
| 9 | C9×#737 | C22 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C3⋊#4207 | — | 3 | 1 | no | — |
| 11 | C3×#4207 | D3 | 1 | 1 | yes | characteristic |
| 12 | D3×#737 | — | 3 | 1 | no | — |
| 13 | C3⋊(C9⋊D9) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #92299 | — | 3 | 2 | no | — |
| 15 | #92299 | — | 6 | 2 | no | — |
| 16 | #92297 | — | 3 | 1 | no | — |
| 17 | #92297 | — | 6 | 1 | no | — |
| 18 | #92296 | — | 6 | 1 | no | — |
| 19 | #92294 | — | 2 | 1 | no | — |
| 20 | C3×C9⋊D9 | — | 3 | 1 | no | — |
| 21 | C9×C3⋊D9 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 22 | D9×3−1+2 | — | 2 | 1 | no | — |
| 23 | D9×3−1+2 | — | 2 | 2 | no | — |
| 24 | D9×3−1+2 | D3 | 1 | 2 | yes | complemented |
| 25 | C9×AGL(1,ℤ/9) | — | 3 | 2 | no | — |
| 26 | D9×H(3,𝔽3) | D3 | 1 | 1 | yes | characteristic |
| 27 | C9×(C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 28 | C3×C9×D9 | — | 2 | 1 | no | — |
| 29 | C3×C9×D9 | — | 3 | 1 | no | — |
| 30 | C3×C9×D9 | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | C3×C9×D9 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 32 | C2×#4207 | — | 9 | 1 | no | — |
| 33 | D3×C3⋊D9 | — | 3 | 1 | no | — |
| 34 | D9×C3⋊D3 | — | 3 | 1 | no | — |
| 35 | D3×AGL(1,ℤ/9) | — | 9 | 2 | no | — |
| 36 | D3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 37 | C3×D3×D9 | — | 9 | 1 | no | — |
| 38 | C3×D3×D9 | — | 9 | 1 | no | — |
| 39 | D92 | — | 3 | 1 | no | — |
| 40 | D92 | — | 3 | 2 | no | — |
| 41 | C3×#737 | C2×D3 | 1 | 1 | yes | characteristic |
| 42 | C9×3−1+2 | — | 2 | 1 | no | — |
| 43 | C9×3−1+2 | — | 2 | 2 | no | — |
| 44 | C9×3−1+2 | — | 2 | 2 | no | — |
| 45 | C9×3−1+2 | — | 4 | 2 | no | — |
| 46 | C9×3−1+2 | — | 4 | 1 | no | — |
| 47 | C9×3−1+2 | C2×D3 | 1 | 2 | yes | complemented |
| 48 | C9×H(3,𝔽3) | — | 2 | 1 | no | — |
| 49 | C9×H(3,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 50 | #6887 | — | 2 | 1 | no | — |
| 51 | #6887 | — | 2 | 1 | no | — |
| 52 | #6887 | — | 4 | 1 | no | — |
| 53 | C3×C92 | — | 2 | 1 | no | — |
| 54 | C3×C92 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 55 | C3×C92 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×#737 | — | 9 | 1 | no | — |
| 57 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 58 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 59 | C3⋊(C3⋊D9) | — | 6 | 1 | no | — |
| 60 | #4207 | — | 2 | 1 | no | — |
| 61 | #4207 | — | 9 | 1 | no | — |
| 62 | #4207 | — | 18 | 1 | no | — |
| 63 | #4207 | — | 18 | 1 | no | — |
| 64 | #4207 | — | 18 | 2 | no | — |
| 65 | #4207 | D9 | 1 | 1 | yes | characteristic, direct product factor |
| 66 | C3⋊AGL(1,ℤ/9) | — | 9 | 2 | no | — |
| 67 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 68 | C9×C3⋊D3 | — | 3 | 1 | no | — |
| 69 | C3×C3⋊D9 | — | 9 | 1 | no | — |
| 70 | C3×C3⋊D9 | — | 9 | 1 | no | — |
| 71 | C3×C3⋊D9 | — | 18 | 1 | no | — |
| 72 | C3×C3⋊D9 | C3×D3 | 1 | 1 | yes | characteristic |
| 73 | D3×3−1+2 | — | 3 | 2 | no | — |
| 74 | D3×3−1+2 | — | 6 | 2 | no | — |
| 75 | D3×3−1+2 | — | 6 | 1 | no | — |
| 76 | C3×AGL(1,ℤ/9) | — | 3 | 2 | no | — |
| 77 | D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 78 | C3×(C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 79 | C3×D3×C9 | — | 3 | 1 | no | — |
| 80 | C3×D3×C9 | — | 3 | 1 | no | — |
| 81 | C3×D3×C9 | — | 6 | 1 | no | — |
| 82 | C3×D3×C9 | — | 9 | 1 | no | — |
| 83 | C32×D9 | — | 2 | 1 | no | — |
| 84 | C32×D9 | — | 3 | 1 | no | — |
| 85 | C32×D9 | C3×D3 | 1 | 1 | yes | characteristic |
| 86 | C32×D9 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 87 | C9⋊D9 | — | 3 | 1 | no | — |
| 88 | C9⋊D9 | — | 3 | 2 | no | — |
| 89 | C9⋊D9 | — | 6 | 1 | no | — |
| 90 | C9⋊D9 | — | 6 | 2 | no | — |
| 91 | D9⋊C9 | — | 6 | 2 | no | — |
| 92 | #4169 | — | 18 | 1 | no | — |
| 93 | #4169 | — | 18 | 2 | no | — |
| 94 | (C3⋊D3)⋊C9 | — | 6 | 1 | no | — |
| 95 | C9×D9 | — | 2 | 2 | no | — |
| 96 | C9×D9 | — | 2 | 1 | no | — |
| 97 | C9×D9 | — | 3 | 1 | no | — |
| 98 | C9×D9 | — | 3 | 2 | no | — |
| 99 | C9×D9 | — | 6 | 1 | no | — |
| 100 | C9×D9 | C3×D3 | 1 | 1 | yes | characteristic |
| 101 | C9×D9 | C3×D3 | 1 | 2 | yes | — |
| 102 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 103 | C3×D32 | — | 27 | 1 | no | — |
| 104 | C2×C3⋊D9 | — | 9 | 1 | no | — |
| 105 | C2×AGL(1,ℤ/9) | — | 27 | 2 | no | — |
| 106 | C2×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 107 | C2×C3×D9 | — | 27 | 1 | no | — |
| 108 | C2×C3×D9 | — | 27 | 1 | no | — |
| 109 | D3×D9 | — | 9 | 1 | no | — |
| 110 | D3×D9 | — | 9 | 2 | no | — |
| 111 | D3×D9 | — | 9 | 1 | no | — |
| 112 | D3×D9 | — | 27 | 1 | no | — |
| 113 | #737 | — | 2 | 2 | no | — |
| 114 | #737 | — | 2 | 1 | no | — |
| 115 | #737 | — | 2 | 1 | no | — |
| 116 | #737 | — | 2 | 1 | no | — |
| 117 | #737 | — | 4 | 1 | no | — |
| 118 | #737 | — | 4 | 1 | no | — |
| 119 | #737 | — | 4 | 2 | no | — |
| 120 | #737 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 121 | C3×3−1+2 | — | 2 | 1 | no | — |
| 122 | C3×3−1+2 | — | 2 | 2 | no | — |
| 123 | C3×3−1+2 | D32 | 1 | 2 | yes | — |
| 124 | C3×H(3,𝔽3) | D32 | 1 | 1 | yes | characteristic |
| 125 | C32×C9 | — | 2 | 1 | no | — |
| 126 | C32×C9 | — | 2 | 1 | no | — |
| 127 | C32×C9 | — | 2 | 1 | no | — |
| 128 | C32×C9 | — | 2 | 1 | no | — |
| 129 | C32×C9 | — | 4 | 1 | no | — |
| 130 | C32×C9 | D32 | 1 | 1 | yes | characteristic |
| 131 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 132 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 133 | C32×C9 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 134 | C9⋊C9 | — | 2 | 2 | no | — |
| 135 | C9⋊C9 | — | 4 | 2 | no | — |
| 136 | C9⋊C9 | — | 4 | 1 | no | — |
| 137 | C9⋊C9 | — | 4 | 2 | no | — |
| 138 | C9⋊C9 | — | 4 | 2 | no | — |
| 139 | C9⋊C9 | — | 4 | 2 | no | — |
| 140 | C9⋊C9 | — | 4 | 2 | no | — |
| 141 | C32⋊C9 | — | 2 | 1 | no | — |
| 142 | C32⋊C9 | — | 2 | 2 | no | — |
| 143 | C32⋊C9 | — | 2 | 1 | no | — |
| 144 | C32⋊C9 | — | 4 | 1 | no | — |
| 145 | C32⋊C9 | — | 4 | 2 | no | — |
| 146 | C32⋊C9 | — | 4 | 1 | no | — |
| 147 | C92 | — | 2 | 1 | no | — |
| 148 | C92 | — | 2 | 2 | no | — |
| 149 | C92 | — | 2 | 1 | no | — |
| 150 | C92 | — | 2 | 2 | no | — |
| 151 | C92 | — | 2 | 1 | no | — |
| 152 | C92 | — | 4 | 1 | no | — |
| 153 | C92 | — | 4 | 2 | no | — |
| 154 | C92 | — | 4 | 1 | no | — |
| 155 | C92 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 156 | C92 | C2×C3×D3 | 1 | 2 | yes | — |
| 157 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 158 | C3×C3⋊D3 | — | 3 | 1 | no | — |
| 159 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 160 | C32×D3 | — | 3 | 1 | no | — |
| 161 | C32×D3 | — | 3 | 1 | no | — |
| 162 | C32×D3 | — | 6 | 1 | no | — |
| 163 | C32×D3 | — | 9 | 1 | no | — |
| 164 | C2×3−1+2 | — | 9 | 2 | no | — |
| 165 | C2×3−1+2 | — | 18 | 2 | no | — |
| 166 | C2×3−1+2 | — | 18 | 1 | no | — |
| 167 | C2×H(3,𝔽3) | — | 9 | 1 | no | — |
| 168 | C2×C3×C9 | — | 9 | 1 | no | — |
| 169 | C2×C3×C9 | — | 9 | 1 | no | — |
| 170 | C2×C3×C9 | — | 18 | 1 | no | — |
| 171 | C2×C3×C9 | — | 27 | 1 | no | — |
| 172 | C3⋊D9 | — | 9 | 1 | no | — |
| 173 | C3⋊D9 | — | 9 | 1 | no | — |
| 174 | C3⋊D9 | — | 9 | 2 | no | — |
| 175 | C3⋊D9 | — | 9 | 1 | no | — |
| 176 | C3⋊D9 | — | 18 | 1 | no | — |
| 177 | C3⋊D9 | — | 18 | 2 | no | — |
| 178 | C3⋊D9 | — | 18 | 1 | no | — |
| 179 | C3⋊D9 | — | 18 | 1 | no | — |
| 180 | C3⋊D9 | — | 18 | 2 | no | — |
| 181 | C3⋊D9 | — | 18 | 1 | no | — |
| 182 | C3⋊D9 | — | 27 | 1 | no | — |
| 183 | C3⋊D9 | — | 54 | 3 | no | — |
| 184 | C3⋊D9 | — | 54 | 1 | no | — |
| 185 | C3⋊D9 | C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 186 | AGL(1,ℤ/9) | — | 3 | 2 | no | — |
| 187 | AGL(1,ℤ/9) | — | 6 | 2 | no | — |
| 188 | AGL(1,ℤ/9) | — | 27 | 2 | no | — |
| 189 | AGL(1,ℤ/9) | — | 54 | 2 | no | — |
| 190 | (C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 191 | (C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 192 | (C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 193 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 194 | D3×C9 | — | 3 | 1 | no | — |
| 195 | D3×C9 | — | 3 | 2 | no | — |
| 196 | D3×C9 | — | 6 | 1 | no | — |
| 197 | D3×C9 | — | 6 | 2 | no | — |
| 198 | D3×C9 | — | 9 | 1 | no | — |
| 199 | D3×C9 | — | 18 | 1 | no | — |
| 200 | D3×C9 | — | 27 | 1 | no | — |
| 201 | C3×D9 | — | 3 | 1 | no | — |
| 202 | C3×D9 | — | 3 | 1 | no | — |
| 203 | C3×D9 | — | 3 | 2 | no | — |
| 204 | C3×D9 | — | 3 | 1 | no | — |
| 205 | C3×D9 | — | 6 | 1 | no | — |
| 206 | C3×D9 | — | 6 | 1 | no | — |
| 207 | C3×D9 | — | 6 | 1 | no | — |
| 208 | C3×D9 | — | 27 | 1 | no | — |
| 209 | C3×D9 | — | 27 | 1 | no | — |
| 210 | C3×D9 | — | 54 | 1 | no | — |
| 211 | C3×D9 | — | 54 | 1 | no | — |
| 212 | C3×D9 | — | 54 | 3 | no | — |
| 213 | C3×D9 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 214 | C2×C3⋊D3 | — | 27 | 1 | no | — |
| 215 | C2×C3×D3 | — | 81 | 1 | no | — |
| 216 | C2×C3×D3 | — | 81 | 1 | no | — |
| 217 | D32 | — | 27 | 1 | no | — |
| 218 | D32 | — | 81 | 1 | no | — |
| 219 | C2×D9 | — | 27 | 1 | no | — |
| 220 | C2×D9 | — | 27 | 2 | no | — |
| 221 | C2×D9 | — | 27 | 1 | no | — |
| 222 | C33 | — | 2 | 1 | no | — |
| 223 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 224 | C33 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 225 | 3−1+2 | — | 2 | 1 | no | — |
| 226 | 3−1+2 | — | 2 | 2 | no | — |
| 227 | 3−1+2 | — | 2 | 2 | no | — |
| 228 | 3−1+2 | — | 2 | 2 | no | — |
| 229 | 3−1+2 | — | 4 | 2 | no | — |
| 230 | 3−1+2 | — | 4 | 2 | no | — |
| 231 | 3−1+2 | — | 4 | 2 | no | — |
| 232 | 3−1+2 | — | 4 | 2 | no | — |
| 233 | 3−1+2 | — | 4 | 2 | no | — |
| 234 | 3−1+2 | — | 4 | 1 | no | — |
| 235 | 3−1+2 | — | 4 | 1 | no | — |
| 236 | 3−1+2 | — | 4 | 2 | no | — |
| 237 | 3−1+2 | D3×D9 | 1 | 2 | yes | complemented |
| 238 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 239 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 240 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 241 | H(3,𝔽3) | D3×D9 | 1 | 1 | yes | characteristic |
| 242 | C3×C9 | — | 2 | 1 | no | — |
| 243 | C3×C9 | — | 2 | 1 | no | — |
| 244 | C3×C9 | — | 2 | 2 | no | — |
| 245 | C3×C9 | — | 2 | 1 | no | — |
| 246 | C3×C9 | — | 2 | 1 | no | — |
| 247 | C3×C9 | — | 2 | 1 | no | — |
| 248 | C3×C9 | — | 2 | 2 | no | — |
| 249 | C3×C9 | — | 2 | 1 | no | — |
| 250 | C3×C9 | — | 2 | 1 | no | — |
| 251 | C3×C9 | — | 2 | 1 | no | — |
| 252 | C3×C9 | — | 2 | 1 | no | — |
| 253 | C3×C9 | — | 2 | 2 | no | — |
| 254 | C3×C9 | — | 3 | 1 | no | — |
| 255 | C3×C9 | — | 4 | 1 | no | — |
| 256 | C3×C9 | — | 4 | 2 | no | — |
| 257 | C3×C9 | — | 4 | 1 | no | — |
| 258 | C3×C9 | — | 4 | 1 | no | — |
| 259 | C3×C9 | — | 4 | 1 | no | — |
| 260 | C3×C9 | — | 4 | 2 | no | — |
| 261 | C3×C9 | — | 4 | 1 | no | — |
| 262 | C3×C9 | — | 6 | 3 | no | — |
| 263 | C3×C9 | — | 6 | 1 | no | — |
| 264 | C3×C9 | — | 6 | 1 | no | — |
| 265 | C3×C9 | — | 6 | 1 | no | — |
| 266 | C3×C9 | — | 12 | 1 | no | — |
| 267 | C3×C9 | — | 12 | 3 | no | — |
| 268 | C3×C9 | — | 12 | 1 | no | — |
| 269 | C3×C9 | — | 12 | 3 | no | — |
| 270 | C3×C9 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 271 | C3×C9 | C2×C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 272 | C3×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 273 | C3×C9 | C3×D32 | 1 | 2 | yes | — |
| 274 | C3×C9 | C2×C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 275 | C2×C32 | — | 9 | 1 | no | — |
| 276 | C2×C32 | — | 9 | 1 | no | — |
| 277 | C2×C32 | — | 18 | 1 | no | — |
| 278 | C2×C32 | — | 27 | 1 | no | — |
| 279 | C3⋊D3 | — | 3 | 1 | no | — |
| 280 | C3⋊D3 | — | 27 | 1 | no | — |
| 281 | C3⋊D3 | — | 27 | 1 | no | — |
| 282 | C3⋊D3 | — | 54 | 1 | no | — |
| 283 | C3⋊D3 | — | 81 | 1 | no | — |
| 284 | C3⋊D3 | — | 162 | 1 | no | — |
| 285 | C3×D3 | — | 3 | 1 | no | — |
| 286 | C3×D3 | — | 9 | 1 | no | — |
| 287 | C3×D3 | — | 9 | 1 | no | — |
| 288 | C3×D3 | — | 9 | 1 | no | — |
| 289 | C3×D3 | — | 9 | 1 | no | — |
| 290 | C3×D3 | — | 18 | 1 | no | — |
| 291 | C3×D3 | — | 18 | 1 | no | — |
| 292 | C3×D3 | — | 27 | 1 | no | — |
| 293 | C3×D3 | — | 81 | 1 | no | — |
| 294 | C3×D3 | — | 81 | 1 | no | — |
| 295 | C3×D3 | — | 162 | 1 | no | — |
| 296 | C2×C9 | — | 9 | 1 | no | — |
| 297 | C2×C9 | — | 9 | 2 | no | — |
| 298 | C2×C9 | — | 18 | 1 | no | — |
| 299 | C2×C9 | — | 18 | 2 | no | — |
| 300 | C2×C9 | — | 27 | 1 | no | — |
| 301 | C2×C9 | — | 54 | 1 | no | — |
| 302 | D9 | — | 3 | 1 | no | — |
| 303 | D9 | — | 3 | 2 | no | — |
| 304 | D9 | — | 27 | 1 | no | — |
| 305 | D9 | — | 27 | 2 | no | — |
| 306 | D9 | — | 27 | 1 | no | — |
| 307 | D9 | — | 54 | 1 | no | — |
| 308 | D9 | — | 54 | 1 | no | — |
| 309 | D9 | — | 54 | 2 | no | — |
| 310 | D9 | — | 54 | 3 | no | — |
| 311 | D9 | — | 162 | 1 | no | — |
| 312 | D9 | — | 162 | 2 | no | — |
| 313 | D9 | #4207 | 1 | 1 | yes | characteristic, direct product factor |
| 314 | C22×C3 | — | 243 | 1 | no | — |
| 315 | C2×D3 | — | 81 | 1 | no | — |
| 316 | C2×D3 | — | 81 | 1 | no | — |
| 317 | C2×D3 | — | 243 | 1 | no | — |
| 318 | C32 | — | 2 | 1 | no | — |
| 319 | C32 | — | 2 | 1 | no | — |
| 320 | C32 | — | 2 | 1 | no | — |
| 321 | C32 | — | 3 | 1 | no | — |
| 322 | C32 | — | 3 | 1 | no | — |
| 323 | C32 | — | 4 | 1 | no | — |
| 324 | C32 | — | 6 | 1 | no | — |
| 325 | C32 | — | 6 | 1 | no | — |
| 326 | C32 | — | 12 | 1 | no | — |
| 327 | C32 | — | 12 | 1 | no | — |
| 328 | C32 | C3×D3×D9 | 1 | 1 | yes | characteristic |
| 329 | C32 | D9×C3⋊D3 | 1 | 1 | yes | characteristic |
| 330 | C32 | C3×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 331 | C9 | — | 2 | 3 | no | — |
| 332 | C9 | — | 2 | 1 | no | — |
| 333 | C9 | — | 2 | 2 | no | — |
| 334 | C9 | — | 2 | 2 | no | — |
| 335 | C9 | — | 2 | 1 | no | — |
| 336 | C9 | — | 2 | 1 | no | — |
| 337 | C9 | — | 4 | 1 | no | — |
| 338 | C9 | — | 4 | 2 | no | — |
| 339 | C9 | — | 6 | 2 | no | — |
| 340 | C9 | — | 6 | 1 | no | — |
| 341 | C9 | — | 6 | 1 | no | — |
| 342 | C9 | — | 12 | 1 | no | — |
| 343 | C9 | — | 12 | 2 | no | — |
| 344 | C9 | — | 12 | 1 | no | — |
| 345 | C9 | C3×D3×D9 | 1 | 1 | yes | characteristic |
| 346 | C9 | C3×D3×D9 | 1 | 2 | yes | — |
| 347 | C9 | C2×#4207 | 1 | 1 | yes | characteristic, complemented |
| 348 | C2×C3 | — | 9 | 1 | no | — |
| 349 | C2×C3 | — | 27 | 1 | no | — |
| 350 | C2×C3 | — | 27 | 1 | no | — |
| 351 | C2×C3 | — | 27 | 1 | no | — |
| 352 | C2×C3 | — | 54 | 1 | no | — |
| 353 | C2×C3 | — | 54 | 1 | no | — |
| 354 | C2×C3 | — | 54 | 1 | no | — |
| 355 | C2×C3 | — | 243 | 1 | no | — |
| 356 | D3 | — | 3 | 1 | no | — |
| 357 | D3 | — | 9 | 1 | no | — |
| 358 | D3 | — | 27 | 1 | no | — |
| 359 | D3 | — | 81 | 1 | no | — |
| 360 | D3 | — | 81 | 1 | no | — |
| 361 | D3 | — | 162 | 1 | no | — |
| 362 | D3 | — | 486 | 1 | no | — |
| 363 | D3 | — | 243 | 1 | no | — |
| 364 | C22 | — | 243 | 1 | no | Sylow |
| 365 | C3 | — | 2 | 1 | no | — |
| 366 | C3 | — | 3 | 1 | no | — |
| 367 | C3 | — | 6 | 1 | no | — |
| 368 | C3 | — | 6 | 1 | no | — |
| 369 | C3 | — | 6 | 1 | no | — |
| 370 | C3 | — | 12 | 1 | no | — |
| 371 | C3 | — | 12 | 1 | no | — |
| 372 | C3 | C3×D9×C3⋊D3 | 1 | 1 | yes | characteristic |
| 373 | C3 | D3×#4207 | 1 | 1 | yes | characteristic |
| 374 | C2 | — | 9 | 1 | no | — |
| 375 | C2 | — | 27 | 1 | no | — |
| 376 | C2 | — | 243 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C92 | C22×C3 |
| Frattini, socle | C32 | C3×D3×C3⋊D3 |
| Fitting | C9×#737 | C22 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13091375 | C2 | semidirect |
| 2. D9×#737 | C2 | semidirect |
| 3. C9×#4207 | C2 | semidirect |
| 5. D9×C3⋊D9 | C3 | semidirect |
| 9. C9×#737 | C22 | semidirect |
| 13. C3⋊(C9⋊D9) | C2×C3 | semidirect |
| 21. C9×C3⋊D9 | C2×C3 | semidirect |
| 24. D9×3−1+2 | D3 | semidirect |
| 30. C3×C9×D9 | D3 | semidirect |
| 31. C3×C9×D9 | C2×C3 | semidirect |
| 47. C9×3−1+2 | C2×D3 | semidirect |
| 54. C3×C92 | C2×D3 | semidirect |
| 55. C3×C92 | C22×C3 | semidirect |
| 65. #4207 | D9 | direct (N × H) |
| 120. #737 | C2×D9 | semidirect |
| 185. C3⋊D9 | C3×D9 | semidirect |
| 237. 3−1+2 | D3×D9 | semidirect |
| 270. C3×C9 | D3×D9 | semidirect |
| 271. C3×C9 | C2×C3×D9 | semidirect |
| 313. D9 | #4207 | direct (N × H) |
| 347. C9 | C2×#4207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13091375 | 2 |
| D9×#737 | 2 |
| C9×#4207 | 2 |
| D3×#4207 | 3 |
| D9×C3⋊D9 | 3 |
| D9×AGL(1,ℤ/9) | 3 |
| D9×(C3⋊D3)⋊C3 | 3 |
| C3×D92 | 3 |