Finite Group DatabasebetaFinite Group DatabasebetaOrder 4374.
2494 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 2494 conjugacy classes of subgroups — too many to draw. Only its 119 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 | #14554289 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C33×#272 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#92285 | C3 | 1 | 3 | yes | maximal, complemented |
| 4 | D3×#6891 | — | 3 | 1 | no | maximal |
| 5 | #13091072 | C3 | 1 | 9 | yes | maximal, complemented |
| 6 | C33×H(3,𝔽3) | C2×C3 | 1 | 1 | yes | characteristic |
| 7 | C3×#6911 | — | 2 | 3 | no | — |
| 8 | C3×#6911 | C2×C3 | 1 | 3 | yes | complemented |
| 9 | C3×#6891 | D3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C3×C32⋊H(3,𝔽3) | — | 2 | 1 | no | — |
| 11 | #10624740 | — | 2 | 9 | no | — |
| 12 | #10624740 | C2×C3 | 1 | 9 | yes | complemented |
| 13 | C34×D3 | — | 3 | 1 | no | — |
| 14 | C34×D3 | — | 9 | 1 | no | — |
| 15 | C32×#272 | — | 3 | 3 | no | — |
| 16 | C32×#272 | C32 | 1 | 1 | yes | characteristic |
| 17 | C32×#272 | C32 | 1 | 3 | yes | complemented |
| 18 | C3×D3×3−1+2 | — | 3 | 3 | no | — |
| 19 | C2×#6891 | — | 9 | 1 | no | — |
| 20 | #92285 | — | 3 | 9 | no | — |
| 21 | C3×#4178 | C32 | 1 | 9 | yes | complemented |
| 22 | D3×C32⋊C9 | — | 3 | 9 | no | — |
| 23 | C35 | — | 3 | 1 | no | — |
| 24 | C35 | C3×D3 | 1 | 1 | yes | characteristic |
| 25 | C32×3−1+2 | C3×D3 | 1 | 3 | yes | complemented |
| 26 | C32×H(3,𝔽3) | — | 2 | 1 | no | — |
| 27 | C32×H(3,𝔽3) | — | 2 | 3 | no | — |
| 28 | C32×H(3,𝔽3) | — | 2 | 3 | no | — |
| 29 | C32×H(3,𝔽3) | — | 3 | 3 | no | — |
| 30 | C32×H(3,𝔽3) | — | 6 | 9 | no | — |
| 31 | C32×H(3,𝔽3) | — | 6 | 3 | no | — |
| 32 | C32×H(3,𝔽3) | — | 6 | 1 | no | — |
| 33 | C32×H(3,𝔽3) | — | 6 | 3 | no | — |
| 34 | C32×H(3,𝔽3) | — | 6 | 3 | no | — |
| 35 | C32×H(3,𝔽3) | C2×C32 | 1 | 1 | yes | characteristic |
| 36 | C32×H(3,𝔽3) | C2×C32 | 1 | 3 | yes | — |
| 37 | #6911 | — | 3 | 9 | no | — |
| 38 | #6911 | — | 6 | 27 | no | — |
| 39 | #6911 | — | 6 | 9 | no | — |
| 40 | C3×#732 | — | 2 | 27 | no | — |
| 41 | C3×#732 | — | 2 | 9 | no | — |
| 42 | C3×#732 | C2×C32 | 1 | 9 | yes | complemented |
| 43 | #6891 | — | 3 | 1 | no | — |
| 44 | #6891 | — | 6 | 3 | no | — |
| 45 | #6891 | — | 6 | 1 | no | — |
| 46 | C32⋊H(3,𝔽3) | — | 2 | 9 | no | — |
| 47 | C32⋊H(3,𝔽3) | — | 6 | 3 | no | — |
| 48 | C32⋊H(3,𝔽3) | — | 6 | 2 | no | — |
| 49 | C32⋊H(3,𝔽3) | — | 6 | 1 | no | — |
| 50 | C3×C32⋊C9 | C3×D3 | 1 | 9 | yes | complemented |
| 51 | C2×C34 | — | 9 | 1 | no | — |
| 52 | C33×D3 | — | 3 | 3 | no | — |
| 53 | C33×D3 | — | 3 | 1 | no | — |
| 54 | C33×D3 | — | 9 | 3 | no | — |
| 55 | C33×D3 | — | 9 | 9 | no | — |
| 56 | C33×D3 | — | 9 | 1 | no | — |
| 57 | C33×D3 | — | 9 | 3 | no | — |
| 58 | C33×D3 | — | 9 | 9 | no | — |
| 59 | C33×D3 | — | 9 | 27 | no | — |
| 60 | C2×C3×3−1+2 | — | 9 | 3 | no | — |
| 61 | C3×#272 | — | 3 | 3 | no | — |
| 62 | C3×#272 | H(3,𝔽3) | 1 | 3 | yes | complemented |
| 63 | C3×#272 | C33 | 1 | 1 | yes | characteristic |
| 64 | D3×3−1+2 | — | 9 | 9 | no | — |
| 65 | C3×D3×C9 | — | 3 | 9 | no | — |
| 66 | C2×C32⋊C9 | — | 9 | 9 | no | — |
| 67 | #4178 | — | 3 | 9 | no | — |
| 68 | C34 | — | 2 | 3 | no | — |
| 69 | C34 | — | 2 | 1 | no | — |
| 70 | C34 | — | 3 | 9 | no | — |
| 71 | C34 | — | 3 | 3 | no | — |
| 72 | C34 | — | 3 | 1 | no | — |
| 73 | C34 | — | 3 | 3 | no | — |
| 74 | C34 | — | 6 | 3 | no | — |
| 75 | C34 | — | 6 | 3 | no | — |
| 76 | C34 | — | 6 | 9 | no | — |
| 77 | C34 | — | 6 | 3 | no | — |
| 78 | C34 | — | 6 | 1 | no | — |
| 79 | C34 | — | 9 | 9 | no | — |
| 80 | C34 | — | 9 | 27 | no | — |
| 81 | C34 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 82 | C34 | C32×D3 | 1 | 1 | yes | characteristic |
| 83 | C34 | C32×D3 | 1 | 3 | yes | — |
| 84 | C3×3−1+2 | — | 3 | 3 | no | — |
| 85 | C3×3−1+2 | — | 3 | 9 | no | — |
| 86 | C3×3−1+2 | — | 6 | 3 | no | — |
| 87 | C3×3−1+2 | — | 6 | 9 | no | — |
| 88 | C3×H(3,𝔽3) | — | 2 | 9 | no | — |
| 89 | C3×H(3,𝔽3) | — | 2 | 3 | no | — |
| 90 | C3×H(3,𝔽3) | — | 2 | 3 | no | — |
| 91 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 92 | C3×H(3,𝔽3) | — | 2 | 9 | no | — |
| 93 | C3×H(3,𝔽3) | — | 3 | 3 | no | — |
| 94 | C3×H(3,𝔽3) | — | 6 | 9 | no | — |
| 95 | C3×H(3,𝔽3) | — | 6 | 18 | no | — |
| 96 | C3×H(3,𝔽3) | — | 6 | 9 | no | — |
| 97 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 98 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 99 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 100 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 101 | C3×H(3,𝔽3) | — | 6 | 2 | no | — |
| 102 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 103 | C3×H(3,𝔽3) | — | 6 | 6 | no | — |
| 104 | C3×H(3,𝔽3) | — | 6 | 27 | no | — |
| 105 | C3×H(3,𝔽3) | — | 6 | 9 | no | — |
| 106 | C3×H(3,𝔽3) | — | 6 | 9 | no | — |
| 107 | C3×H(3,𝔽3) | — | 6 | 54 | no | — |
| 108 | C3×H(3,𝔽3) | — | 6 | 9 | no | — |
| 109 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 110 | C3×H(3,𝔽3) | — | 6 | 18 | no | — |
| 111 | C3×H(3,𝔽3) | — | 6 | 9 | no | — |
| 112 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 113 | C3×H(3,𝔽3) | — | 6 | 18 | no | — |
| 114 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 115 | C3×H(3,𝔽3) | — | 6 | 9 | no | — |
| 116 | C3×H(3,𝔽3) | — | 18 | 27 | no | — |
| 117 | C3×H(3,𝔽3) | C2×H(3,𝔽3) | 1 | 3 | yes | — |
| 118 | C3×H(3,𝔽3) | C2×C33 | 1 | 1 | yes | characteristic |
| 119 | C32×C9 | C32×D3 | 1 | 9 | yes | complemented |
| 120 | #732 | — | 3 | 9 | no | — |
| 121 | #732 | — | 6 | 9 | no | — |
| 122 | #732 | — | 6 | 27 | no | — |
| 123 | #732 | — | 6 | 81 | no | — |
| 124 | C32⋊C9 | — | 3 | 9 | no | — |
| 125 | C32⋊C9 | — | 6 | 9 | no | — |
| 126 | C2×C33 | — | 9 | 3 | no | — |
| 127 | C2×C33 | — | 9 | 1 | no | — |
| 128 | C2×C33 | — | 27 | 3 | no | — |
| 129 | C2×C33 | — | 27 | 9 | no | — |
| 130 | C32×D3 | — | 3 | 1 | no | — |
| 131 | C32×D3 | — | 3 | 9 | no | — |
| 132 | C32×D3 | — | 3 | 3 | no | — |
| 133 | C32×D3 | — | 9 | 3 | no | — |
| 134 | C32×D3 | — | 9 | 6 | no | — |
| 135 | C32×D3 | — | 9 | 3 | no | — |
| 136 | C32×D3 | — | 9 | 3 | no | — |
| 137 | C32×D3 | — | 9 | 1 | no | — |
| 138 | C32×D3 | — | 9 | 9 | no | — |
| 139 | C32×D3 | — | 9 | 9 | no | — |
| 140 | C32×D3 | — | 9 | 27 | no | — |
| 141 | C32×D3 | — | 9 | 9 | no | — |
| 142 | C32×D3 | — | 9 | 18 | no | — |
| 143 | C32×D3 | — | 9 | 81 | no | — |
| 144 | C2×3−1+2 | — | 27 | 9 | no | — |
| 145 | C2×C3×C9 | — | 9 | 9 | no | — |
| 146 | #272 | C3×H(3,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 147 | D3×C9 | — | 9 | 9 | no | — |
| 148 | C33 | — | 2 | 1 | no | — |
| 149 | C33 | — | 2 | 3 | no | — |
| 150 | C33 | — | 2 | 3 | no | — |
| 151 | C33 | — | 3 | 3 | no | — |
| 152 | C33 | — | 3 | 9 | no | — |
| 153 | C33 | — | 3 | 9 | no | — |
| 154 | C33 | — | 3 | 3 | no | — |
| 155 | C33 | — | 3 | 1 | no | — |
| 156 | C33 | — | 3 | 3 | no | — |
| 157 | C33 | — | 3 | 9 | no | — |
| 158 | C33 | — | 6 | 9 | no | — |
| 159 | C33 | — | 6 | 3 | no | — |
| 160 | C33 | — | 6 | 27 | no | — |
| 161 | C33 | — | 6 | 9 | no | — |
| 162 | C33 | — | 6 | 9 | no | — |
| 163 | C33 | — | 6 | 3 | no | — |
| 164 | C33 | — | 6 | 3 | no | — |
| 165 | C33 | — | 6 | 9 | no | — |
| 166 | C33 | — | 6 | 3 | no | — |
| 167 | C33 | — | 6 | 1 | no | — |
| 168 | C33 | — | 6 | 9 | no | — |
| 169 | C33 | — | 9 | 3 | no | — |
| 170 | C33 | — | 9 | 6 | no | — |
| 171 | C33 | — | 9 | 27 | no | — |
| 172 | C33 | — | 9 | 81 | no | — |
| 173 | C33 | — | 9 | 9 | no | — |
| 174 | C33 | — | 9 | 18 | no | — |
| 175 | C33 | — | 9 | 9 | no | — |
| 176 | C33 | — | 18 | 9 | no | — |
| 177 | C33 | — | 18 | 6 | no | — |
| 178 | C33 | — | 18 | 3 | no | — |
| 179 | C33 | — | 18 | 27 | no | — |
| 180 | C33 | — | 18 | 81 | no | — |
| 181 | C33 | — | 18 | 9 | no | — |
| 182 | C33 | — | 18 | 18 | no | — |
| 183 | C33 | — | 18 | 27 | no | — |
| 184 | C33 | — | 18 | 9 | no | — |
| 185 | C33 | C3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 186 | C33 | C3×(C3⋊D3)⋊C3 | 1 | 3 | yes | — |
| 187 | C33 | D3×H(3,𝔽3) | 1 | 3 | yes | — |
| 188 | C33 | C33×D3 | 1 | 1 | yes | characteristic |
| 189 | 3−1+2 | — | 9 | 9 | no | — |
| 190 | 3−1+2 | — | 18 | 9 | no | — |
| 191 | H(3,𝔽3) | — | 2 | 9 | no | — |
| 192 | H(3,𝔽3) | — | 2 | 3 | no | — |
| 193 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 194 | H(3,𝔽3) | — | 6 | 3 | no | — |
| 195 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 196 | H(3,𝔽3) | — | 6 | 2 | no | — |
| 197 | H(3,𝔽3) | — | 6 | 3 | no | — |
| 198 | H(3,𝔽3) | — | 6 | 18 | no | — |
| 199 | H(3,𝔽3) | — | 6 | 6 | no | — |
| 200 | H(3,𝔽3) | — | 6 | 18 | no | — |
| 201 | H(3,𝔽3) | — | 6 | 9 | no | — |
| 202 | H(3,𝔽3) | — | 6 | 9 | no | — |
| 203 | H(3,𝔽3) | — | 6 | 54 | no | — |
| 204 | H(3,𝔽3) | — | 6 | 9 | no | — |
| 205 | H(3,𝔽3) | — | 6 | 3 | no | — |
| 206 | H(3,𝔽3) | — | 6 | 9 | no | — |
| 207 | H(3,𝔽3) | — | 18 | 9 | no | — |
| 208 | H(3,𝔽3) | — | 18 | 54 | no | — |
| 209 | H(3,𝔽3) | — | 18 | 9 | no | — |
| 210 | H(3,𝔽3) | — | 18 | 27 | no | — |
| 211 | H(3,𝔽3) | C2×C3×H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 212 | C3×C9 | — | 3 | 9 | no | — |
| 213 | C3×C9 | — | 3 | 9 | no | — |
| 214 | C3×C9 | — | 6 | 9 | no | — |
| 215 | C2×C32 | — | 9 | 1 | no | — |
| 216 | C2×C32 | — | 9 | 3 | no | — |
| 217 | C2×C32 | — | 9 | 9 | no | — |
| 218 | C2×C32 | — | 27 | 6 | no | — |
| 219 | C2×C32 | — | 27 | 3 | no | — |
| 220 | C2×C32 | — | 27 | 3 | no | — |
| 221 | C2×C32 | — | 27 | 27 | no | — |
| 222 | C3×D3 | — | 3 | 3 | no | — |
| 223 | C3×D3 | — | 3 | 1 | no | — |
| 224 | C3×D3 | — | 9 | 3 | no | — |
| 225 | C3×D3 | — | 9 | 9 | no | — |
| 226 | C3×D3 | — | 9 | 1 | no | — |
| 227 | C3×D3 | — | 9 | 3 | no | — |
| 228 | C3×D3 | — | 9 | 9 | no | — |
| 229 | C3×D3 | — | 9 | 27 | no | — |
| 230 | C2×C9 | — | 27 | 9 | no | — |
| 231 | C32 | — | 2 | 1 | no | — |
| 232 | C32 | — | 2 | 3 | no | — |
| 233 | C32 | — | 3 | 27 | no | — |
| 234 | C32 | — | 3 | 3 | no | — |
| 235 | C32 | — | 3 | 6 | no | — |
| 236 | C32 | — | 3 | 3 | no | — |
| 237 | C32 | — | 3 | 3 | no | — |
| 238 | C32 | — | 3 | 1 | no | — |
| 239 | C32 | — | 6 | 3 | no | — |
| 240 | C32 | — | 6 | 6 | no | — |
| 241 | C32 | — | 6 | 3 | no | — |
| 242 | C32 | — | 6 | 9 | no | — |
| 243 | C32 | — | 6 | 3 | no | — |
| 244 | C32 | — | 6 | 1 | no | — |
| 245 | C32 | — | 6 | 3 | no | — |
| 246 | C32 | — | 9 | 3 | no | — |
| 247 | C32 | — | 9 | 9 | no | — |
| 248 | C32 | — | 9 | 9 | no | — |
| 249 | C32 | — | 9 | 27 | no | — |
| 250 | C32 | — | 9 | 3 | no | — |
| 251 | C32 | — | 18 | 3 | no | — |
| 252 | C32 | — | 18 | 9 | no | — |
| 253 | C32 | — | 18 | 27 | no | — |
| 254 | C32 | — | 18 | 9 | no | — |
| 255 | C32 | — | 18 | 27 | no | — |
| 256 | C32 | — | 18 | 9 | no | — |
| 257 | C32 | — | 18 | 81 | no | — |
| 258 | C32 | — | 18 | 27 | no | — |
| 259 | C32 | — | 18 | 6 | no | — |
| 260 | C32 | — | 18 | 3 | no | — |
| 261 | C32 | — | 18 | 3 | no | — |
| 262 | C32 | — | 18 | 27 | no | — |
| 263 | C32 | — | 18 | 9 | no | — |
| 264 | C32 | — | 54 | 27 | no | — |
| 265 | C32 | (C3⋊D3)⋊H(3,𝔽3) | 1 | 3 | yes | — |
| 266 | C32 | #92285 | 1 | 9 | yes | complemented |
| 267 | C32 | C32×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 268 | C32 | C3×D3×H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 269 | C9 | — | 9 | 9 | no | — |
| 270 | C2×C3 | — | 9 | 3 | no | — |
| 271 | C2×C3 | — | 9 | 1 | no | — |
| 272 | C2×C3 | — | 27 | 3 | no | — |
| 273 | C2×C3 | — | 27 | 9 | no | — |
| 274 | D3 | — | 3 | 1 | no | — |
| 275 | D3 | — | 9 | 1 | no | — |
| 276 | C3 | — | 3 | 1 | no | — |
| 277 | C3 | — | 3 | 3 | no | — |
| 278 | C3 | — | 3 | 9 | no | — |
| 279 | C3 | — | 6 | 1 | no | — |
| 280 | C3 | — | 6 | 3 | no | — |
| 281 | C3 | — | 9 | 1 | no | — |
| 282 | C3 | — | 18 | 3 | no | — |
| 283 | C3 | — | 18 | 9 | no | — |
| 284 | C3 | — | 18 | 3 | no | — |
| 285 | C3 | — | 18 | 1 | no | — |
| 286 | C3 | — | 54 | 9 | no | — |
| 287 | C3 | C3×(C3⋊D3)⋊H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 288 | C3 | C3×#92285 | 1 | 3 | yes | — |
| 289 | C2 | — | 9 | 1 | no | Sylow |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14554289 | C2 | semidirect |
| 2. C33×#272 | C3 | semidirect |
| 3. C3×#92285 | C3 | semidirect |
| 5. #13091072 | C3 | semidirect |
| 8. C3×#6911 | C2×C3 | semidirect |
| 9. C3×#6891 | D3 | semidirect |
| 12. #10624740 | C2×C3 | semidirect |
| 17. C32×#272 | C32 | semidirect |
| 21. C3×#4178 | C32 | semidirect |
| 25. C32×3−1+2 | C3×D3 | semidirect |
| 42. C3×#732 | C2×C32 | semidirect |
| 50. C3×C32⋊C9 | C3×D3 | semidirect |
| 62. C3×#272 | H(3,𝔽3) | semidirect |
| 119. C32×C9 | C32×D3 | semidirect |
| 146. #272 | C3×H(3,𝔽3) | semidirect |
| 266. C32 | #92285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14554289 | 2 |
| C33×#272 | 3 |
| C3×#92285 | 3 |
| D3×#6891 | 3 |
| #13091072 | 3 |