Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
864 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 149 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 | #11721711 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C9×#876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#63438 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11721051 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11721039 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11721005 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11720997 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10594023 | — | 3 | 1 | no | maximal |
| 9 | #10589813 | — | 3 | 1 | no | maximal |
| 10 | C22×D3×D9 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C4⋊(C3⋊D9) | C22 | 1 | 3 | yes | — |
| 12 | C2×C4⋊(C3⋊D9) | C22 | 1 | 3 | yes | complemented |
| 13 | C2×#6195 | C22 | 1 | 3 | yes | — |
| 14 | C2×#6192 | C22 | 1 | 3 | yes | — |
| 15 | C2×(C3⋊D9)⋊C4 | C22 | 1 | 3 | yes | complemented |
| 16 | C3×C42×C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C9×(C2×D3)⋊C4 | C22 | 1 | 3 | yes | — |
| 18 | C3×(C2×D9)⋊C4 | C22 | 1 | 3 | yes | — |
| 19 | C9×Dic3⋊C4 | C22 | 1 | 3 | yes | complemented |
| 20 | C3×Dic9⋊C4 | C22 | 1 | 3 | yes | complemented |
| 21 | #88445 | C22 | 1 | 3 | yes | — |
| 22 | #88445 | C22 | 1 | 3 | yes | complemented |
| 23 | #64083 | — | 3 | 1 | no | — |
| 24 | C3×#876 | — | 3 | 1 | no | — |
| 25 | C3×#876 | D3 | 1 | 1 | yes | characteristic |
| 26 | #63923 | — | 3 | 3 | no | — |
| 27 | #63910 | — | 3 | 3 | no | — |
| 28 | #63910 | — | 3 | 3 | no | — |
| 29 | #63897 | — | 3 | 3 | no | — |
| 30 | C9×#126 | — | 3 | 1 | no | — |
| 31 | #63457 | — | 3 | 3 | no | — |
| 32 | #63456 | — | 3 | 3 | no | — |
| 33 | #63446 | — | 3 | 3 | no | — |
| 34 | #63444 | — | 3 | 3 | no | — |
| 35 | #63438 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | #63436 | — | 3 | 1 | no | — |
| 37 | #63436 | — | 6 | 1 | no | — |
| 38 | C22×C3⋊D9 | C23 | 1 | 1 | yes | characteristic |
| 39 | C22×C3⋊D9 | C23 | 1 | 3 | yes | — |
| 40 | C22×D3×C9 | C23 | 1 | 1 | yes | characteristic |
| 41 | C22×C3×D9 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×D3×D9 | — | 4 | 3 | no | — |
| 43 | C2×C3×C4×C9 | C23 | 1 | 3 | yes | — |
| 44 | C4⋊(C3⋊D9) | — | 4 | 3 | no | — |
| 45 | C4⋊(C3⋊D9) | — | 4 | 3 | no | — |
| 46 | C2×C9×Dic3 | C23 | 1 | 3 | yes | — |
| 47 | C2×C3×Dic9 | C23 | 1 | 3 | yes | — |
| 48 | #6195 | — | 4 | 3 | no | — |
| 49 | #6192 | — | 4 | 3 | no | — |
| 50 | (C3⋊D9)⋊C4 | — | 4 | 3 | no | — |
| 51 | #5711 | — | 9 | 1 | no | — |
| 52 | #5711 | — | 9 | 1 | no | — |
| 53 | C22×D32 | — | 3 | 1 | no | — |
| 54 | C2×C4⋊(C3⋊D3) | — | 3 | 3 | no | — |
| 55 | C2×C4⋊(C3⋊D3) | — | 3 | 3 | no | — |
| 56 | C2×#626 | — | 3 | 3 | no | — |
| 57 | C2×#626 | — | 3 | 3 | no | — |
| 58 | C2×#624 | — | 3 | 3 | no | — |
| 59 | C23×D9 | — | 3 | 1 | no | — |
| 60 | C32×C42 | C2×D3 | 1 | 1 | yes | characteristic |
| 61 | C3×(C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 62 | C3×(C2×D3)⋊C4 | C2×D3 | 1 | 3 | yes | — |
| 63 | C3×Dic3⋊C4 | — | 3 | 3 | no | — |
| 64 | C3×Dic3⋊C4 | C2×D3 | 1 | 3 | yes | — |
| 65 | #3722 | — | 3 | 3 | no | — |
| 66 | #3722 | — | 3 | 3 | no | — |
| 67 | C2×#611 | — | 3 | 3 | no | — |
| 68 | C2×D36 | — | 3 | 3 | no | — |
| 69 | C2×D36 | — | 3 | 3 | no | — |
| 70 | C2×D36 | — | 3 | 3 | no | — |
| 71 | C2×D36 | — | 6 | 3 | no | — |
| 72 | C2×D36 | — | 6 | 3 | no | — |
| 73 | C2×C4×D9 | — | 3 | 3 | no | — |
| 74 | C9×C4⋊C4 | — | 3 | 3 | no | — |
| 75 | C9×C22⋊C4 | — | 3 | 3 | no | — |
| 76 | C42×C9 | — | 2 | 1 | no | — |
| 77 | C42×C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 78 | (C2×D9)⋊C4 | — | 3 | 3 | no | — |
| 79 | (C2×D9)⋊C4 | — | 3 | 3 | no | — |
| 80 | (C2×D9)⋊C4 | C2×D3 | 1 | 3 | yes | — |
| 81 | Dic9⋊C4 | C2×D3 | 1 | 3 | yes | complemented |
| 82 | C22×C3×C9 | C24 | 1 | 1 | yes | characteristic |
| 83 | C2×C3⋊D9 | — | 2 | 3 | no | — |
| 84 | C2×C3⋊D9 | — | 2 | 3 | no | — |
| 85 | C2×C3⋊D9 | — | 2 | 3 | no | — |
| 86 | C2×C3⋊D9 | — | 2 | 3 | no | — |
| 87 | C2×D3×C9 | — | 2 | 3 | no | — |
| 88 | C2×C3×D9 | — | 2 | 3 | no | — |
| 89 | D3×D9 | — | 4 | 4 | no | — |
| 90 | C3×C4×C9 | — | 2 | 3 | no | — |
| 91 | C9×Dic3 | — | 2 | 3 | no | — |
| 92 | C3×Dic9 | — | 2 | 3 | no | — |
| 93 | C3×#126 | — | 3 | 1 | no | — |
| 94 | C3×#126 | — | 9 | 1 | no | — |
| 95 | #895 | — | 9 | 3 | no | — |
| 96 | #895 | — | 9 | 3 | no | — |
| 97 | #894 | — | 9 | 3 | no | — |
| 98 | #894 | — | 9 | 3 | no | — |
| 99 | #884 | — | 9 | 3 | no | — |
| 100 | #884 | — | 9 | 3 | no | — |
| 101 | #882 | — | 9 | 3 | no | — |
| 102 | #882 | — | 9 | 3 | no | — |
| 103 | #876 | — | 3 | 1 | no | — |
| 104 | #876 | D9 | 1 | 1 | yes | characteristic, complemented |
| 105 | #874 | — | 9 | 1 | no | — |
| 106 | #874 | — | 9 | 1 | no | — |
| 107 | #874 | — | 18 | 1 | no | — |
| 108 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 109 | C22×C3⋊D3 | — | 3 | 3 | no | — |
| 110 | C22×C3×D3 | — | 3 | 1 | no | — |
| 111 | C22×C3×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 112 | C2×D32 | — | 12 | 3 | no | — |
| 113 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 114 | C4⋊(C3⋊D3) | — | 12 | 3 | no | — |
| 115 | C4⋊(C3⋊D3) | — | 12 | 3 | no | — |
| 116 | C2×C3×Dic3 | — | 3 | 3 | no | — |
| 117 | C2×C3×Dic3 | C22×D3 | 1 | 3 | yes | — |
| 118 | #626 | — | 12 | 3 | no | — |
| 119 | #626 | — | 12 | 3 | no | — |
| 120 | #624 | — | 12 | 3 | no | — |
| 121 | C23×C9 | — | 3 | 1 | no | — |
| 122 | C22×D9 | — | 3 | 1 | no | — |
| 123 | C22×D9 | — | 3 | 3 | no | — |
| 124 | C22×D9 | — | 6 | 1 | no | — |
| 125 | C22×D9 | — | 6 | 3 | no | — |
| 126 | C22×D9 | — | 12 | 3 | no | — |
| 127 | C22×D9 | C22×D3 | 1 | 1 | yes | characteristic |
| 128 | C2×C4×C9 | — | 2 | 3 | no | — |
| 129 | C2×C4×C9 | — | 3 | 3 | no | — |
| 130 | C2×C4×C9 | C22×D3 | 1 | 3 | yes | — |
| 131 | #611 | — | 12 | 3 | no | — |
| 132 | C2×Dic9 | C22×D3 | 1 | 3 | yes | — |
| 133 | D36 | — | 12 | 3 | no | — |
| 134 | D36 | — | 12 | 3 | no | — |
| 135 | D36 | — | 12 | 6 | no | — |
| 136 | D36 | — | 12 | 6 | no | — |
| 137 | D36 | — | 12 | 3 | no | — |
| 138 | C4×D9 | — | 12 | 3 | no | — |
| 139 | #560 | — | 27 | 1 | no | Sylow |
| 140 | C2×C3×C9 | H(5,𝔽2) | 1 | 3 | yes | — |
| 141 | C3⋊D9 | — | 4 | 1 | no | — |
| 142 | C3⋊D9 | — | 4 | 3 | no | — |
| 143 | D3×C9 | — | 4 | 1 | no | — |
| 144 | C3×D9 | — | 4 | 1 | no | — |
| 145 | C23×D3 | — | 9 | 1 | no | — |
| 146 | C23×D3 | — | 9 | 1 | no | — |
| 147 | C2×#67 | — | 9 | 3 | no | — |
| 148 | C2×#67 | — | 9 | 3 | no | — |
| 149 | C2×D12 | — | 9 | 3 | no | — |
| 150 | C2×D12 | — | 9 | 3 | no | — |
| 151 | C2×D12 | — | 9 | 3 | no | — |
| 152 | C2×D12 | — | 9 | 3 | no | — |
| 153 | C2×D12 | — | 9 | 3 | no | — |
| 154 | C2×D12 | — | 9 | 3 | no | — |
| 155 | C2×D12 | — | 18 | 3 | no | — |
| 156 | C2×D12 | — | 18 | 3 | no | — |
| 157 | C2×C4×D3 | — | 9 | 3 | no | — |
| 158 | C2×C4×D3 | — | 9 | 3 | no | — |
| 159 | C3×C4⋊C4 | — | 3 | 3 | no | — |
| 160 | C3×C4⋊C4 | — | 9 | 3 | no | — |
| 161 | C3×C22⋊C4 | — | 3 | 3 | no | — |
| 162 | C3×C22⋊C4 | — | 9 | 3 | no | — |
| 163 | C3×C42 | — | 2 | 1 | no | — |
| 164 | C3×C42 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 165 | C3×C42 | D32 | 1 | 1 | yes | characteristic |
| 166 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 167 | (C2×D3)⋊C4 | — | 9 | 3 | no | — |
| 168 | (C2×D3)⋊C4 | — | 9 | 3 | no | — |
| 169 | (C2×D3)⋊C4 | — | 9 | 3 | no | — |
| 170 | (C2×D3)⋊C4 | — | 9 | 3 | no | — |
| 171 | (C2×D3)⋊C4 | C2×D9 | 1 | 3 | yes | — |
| 172 | Dic3⋊C4 | — | 3 | 3 | no | — |
| 173 | Dic3⋊C4 | C2×D9 | 1 | 3 | yes | complemented |
| 174 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 175 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 176 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 177 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 178 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 179 | C2×C3×D3 | — | 2 | 3 | no | — |
| 180 | C2×C3×D3 | — | 6 | 3 | no | — |
| 181 | D32 | — | 12 | 4 | no | — |
| 182 | C32×C4 | — | 2 | 3 | no | — |
| 183 | C3×Dic3 | — | 2 | 3 | no | — |
| 184 | C3×Dic3 | — | 6 | 3 | no | — |
| 185 | C22×C9 | — | 2 | 1 | no | — |
| 186 | C22×C9 | — | 6 | 3 | no | — |
| 187 | C22×C9 | C23×D3 | 1 | 1 | yes | characteristic |
| 188 | C2×D9 | — | 2 | 3 | no | — |
| 189 | C2×D9 | — | 6 | 3 | no | — |
| 190 | C2×D9 | — | 6 | 3 | no | — |
| 191 | C2×D9 | — | 6 | 3 | no | — |
| 192 | C2×D9 | — | 6 | 3 | no | — |
| 193 | C2×D9 | — | 12 | 3 | no | — |
| 194 | C2×D9 | — | 12 | 3 | no | — |
| 195 | C2×D9 | — | 12 | 3 | no | — |
| 196 | C2×D9 | — | 12 | 3 | no | — |
| 197 | C2×D9 | — | 12 | 4 | no | — |
| 198 | C4×C9 | — | 2 | 6 | no | — |
| 199 | C4×C9 | — | 2 | 3 | no | — |
| 200 | C4×C9 | — | 6 | 3 | no | — |
| 201 | Dic9 | — | 2 | 3 | no | — |
| 202 | #127 | — | 27 | 1 | no | — |
| 203 | #126 | — | 3 | 1 | no | — |
| 204 | #126 | — | 9 | 1 | no | — |
| 205 | #123 | — | 27 | 3 | no | — |
| 206 | #121 | — | 27 | 3 | no | — |
| 207 | #121 | — | 27 | 3 | no | — |
| 208 | #120 | — | 27 | 3 | no | — |
| 209 | C3×C9 | #560 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 210 | C23×C3 | — | 3 | 1 | no | — |
| 211 | C23×C3 | — | 9 | 1 | no | — |
| 212 | C22×D3 | — | 3 | 1 | no | — |
| 213 | C22×D3 | — | 9 | 1 | no | — |
| 214 | C22×D3 | — | 9 | 3 | no | — |
| 215 | C22×D3 | — | 9 | 1 | no | — |
| 216 | C22×D3 | — | 9 | 3 | no | — |
| 217 | C22×D3 | — | 18 | 1 | no | — |
| 218 | C22×D3 | — | 18 | 3 | no | — |
| 219 | C22×D3 | — | 36 | 3 | no | — |
| 220 | C22×D3 | — | 36 | 3 | no | — |
| 221 | C22×D3 | C22×D9 | 1 | 1 | yes | characteristic |
| 222 | C2×C3×C4 | — | 2 | 3 | no | — |
| 223 | C2×C3×C4 | — | 3 | 3 | no | — |
| 224 | C2×C3×C4 | — | 9 | 3 | no | — |
| 225 | C2×C3×C4 | C22×D9 | 1 | 3 | yes | — |
| 226 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 227 | #67 | — | 36 | 3 | no | — |
| 228 | #67 | — | 36 | 3 | no | — |
| 229 | C2×Dic3 | — | 3 | 3 | no | — |
| 230 | C2×Dic3 | C22×D9 | 1 | 3 | yes | — |
| 231 | D12 | — | 36 | 3 | no | — |
| 232 | D12 | — | 36 | 3 | no | — |
| 233 | D12 | — | 36 | 3 | no | — |
| 234 | D12 | — | 36 | 3 | no | — |
| 235 | D12 | — | 36 | 6 | no | — |
| 236 | D12 | — | 36 | 6 | no | — |
| 237 | D12 | — | 36 | 3 | no | — |
| 238 | D12 | — | 36 | 3 | no | — |
| 239 | C4×D3 | — | 36 | 3 | no | — |
| 240 | C4×D3 | — | 36 | 3 | no | — |
| 241 | C2×C32 | #1009 | 1 | 3 | yes | — |
| 242 | C3⋊D3 | — | 12 | 1 | no | — |
| 243 | C3⋊D3 | — | 12 | 3 | no | — |
| 244 | C3×D3 | — | 4 | 1 | no | — |
| 245 | C3×D3 | — | 12 | 1 | no | — |
| 246 | C2×C9 | — | 2 | 3 | no | — |
| 247 | C2×C9 | — | 12 | 1 | no | — |
| 248 | C2×C9 | #1009 | 1 | 3 | yes | — |
| 249 | D9 | — | 4 | 1 | no | — |
| 250 | D9 | — | 12 | 3 | no | — |
| 251 | D9 | — | 12 | 1 | no | — |
| 252 | D9 | — | 24 | 1 | no | — |
| 253 | D9 | — | 24 | 3 | no | — |
| 254 | C24 | — | 27 | 1 | no | — |
| 255 | C2×D4 | — | 27 | 3 | no | — |
| 256 | C2×D4 | — | 27 | 3 | no | — |
| 257 | C2×D4 | — | 27 | 3 | no | — |
| 258 | C2×D4 | — | 27 | 3 | no | — |
| 259 | C22×C4 | — | 27 | 3 | no | — |
| 260 | C4⋊C4 | — | 3 | 3 | no | — |
| 261 | C4⋊C4 | — | 9 | 3 | no | — |
| 262 | C22⋊C4 | — | 3 | 3 | no | — |
| 263 | C22⋊C4 | — | 9 | 3 | no | — |
| 264 | C22⋊C4 | — | 27 | 3 | no | — |
| 265 | C22⋊C4 | — | 27 | 3 | no | — |
| 266 | C42 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 267 | C22×C3 | — | 2 | 1 | no | — |
| 268 | C22×C3 | — | 6 | 3 | no | — |
| 269 | C22×C3 | — | 18 | 3 | no | — |
| 270 | C22×C3 | C23×D9 | 1 | 1 | yes | characteristic |
| 271 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 272 | C2×D3 | — | 2 | 3 | no | — |
| 273 | C2×D3 | — | 6 | 3 | no | — |
| 274 | C2×D3 | — | 18 | 3 | no | — |
| 275 | C2×D3 | — | 18 | 3 | no | — |
| 276 | C2×D3 | — | 18 | 3 | no | — |
| 277 | C2×D3 | — | 18 | 3 | no | — |
| 278 | C2×D3 | — | 18 | 3 | no | — |
| 279 | C2×D3 | — | 18 | 3 | no | — |
| 280 | C2×D3 | — | 18 | 3 | no | — |
| 281 | C2×D3 | — | 18 | 3 | no | — |
| 282 | C2×D3 | — | 36 | 3 | no | — |
| 283 | C2×D3 | — | 36 | 3 | no | — |
| 284 | C2×D3 | — | 36 | 3 | no | — |
| 285 | C2×D3 | — | 36 | 3 | no | — |
| 286 | C2×D3 | — | 36 | 4 | no | — |
| 287 | C2×D3 | — | 36 | 4 | no | — |
| 288 | C3×C4 | — | 2 | 6 | no | — |
| 289 | C3×C4 | — | 2 | 3 | no | — |
| 290 | C3×C4 | — | 2 | 3 | no | — |
| 291 | C3×C4 | — | 6 | 3 | no | — |
| 292 | C3×C4 | — | 18 | 3 | no | — |
| 293 | Dic3 | — | 2 | 3 | no | — |
| 294 | Dic3 | — | 6 | 3 | no | — |
| 295 | C32 | #5711 | 1 | 1 | yes | characteristic |
| 296 | C9 | — | 2 | 1 | no | — |
| 297 | C9 | #5711 | 1 | 1 | yes | characteristic, complemented |
| 298 | C23 | — | 3 | 1 | no | — |
| 299 | C23 | — | 9 | 1 | no | — |
| 300 | C23 | — | 27 | 1 | no | — |
| 301 | C23 | — | 27 | 3 | no | — |
| 302 | C23 | — | 108 | 3 | no | — |
| 303 | D4 | — | 108 | 3 | no | — |
| 304 | D4 | — | 108 | 3 | no | — |
| 305 | D4 | — | 108 | 3 | no | — |
| 306 | D4 | — | 108 | 3 | no | — |
| 307 | C2×C4 | — | 3 | 3 | no | — |
| 308 | C2×C4 | — | 9 | 3 | no | — |
| 309 | C2×C4 | — | 108 | 3 | no | — |
| 310 | C2×C4 | C2×D3×D9 | 1 | 3 | yes | — |
| 311 | C2×C3 | — | 2 | 3 | no | — |
| 312 | C2×C3 | — | 12 | 1 | no | — |
| 313 | C2×C3 | — | 36 | 1 | no | — |
| 314 | C2×C3 | #63715 | 1 | 3 | yes | — |
| 315 | C2×C3 | #64308 | 1 | 3 | yes | — |
| 316 | D3 | — | 4 | 1 | no | — |
| 317 | D3 | — | 12 | 1 | no | — |
| 318 | D3 | — | 36 | 1 | no | — |
| 319 | D3 | — | 36 | 3 | no | — |
| 320 | D3 | — | 36 | 1 | no | — |
| 321 | D3 | — | 36 | 3 | no | — |
| 322 | D3 | — | 72 | 1 | no | — |
| 323 | D3 | — | 72 | 3 | no | — |
| 324 | C22 | — | 6 | 3 | no | — |
| 325 | C22 | — | 18 | 3 | no | — |
| 326 | C22 | — | 54 | 3 | no | — |
| 327 | C22 | — | 54 | 3 | no | — |
| 328 | C22 | — | 54 | 3 | no | — |
| 329 | C22 | — | 54 | 3 | no | — |
| 330 | C22 | — | 108 | 4 | no | — |
| 331 | C22 | C22×D3×D9 | 1 | 1 | yes | characteristic |
| 332 | C4 | — | 2 | 3 | no | — |
| 333 | C4 | — | 6 | 3 | no | — |
| 334 | C4 | — | 18 | 3 | no | — |
| 335 | C3 | — | 2 | 1 | no | — |
| 336 | C3 | #10589813 | 1 | 1 | yes | characteristic, complemented |
| 337 | C3 | #10594023 | 1 | 1 | yes | characteristic |
| 338 | C2 | — | 12 | 1 | no | — |
| 339 | C2 | — | 36 | 1 | no | — |
| 340 | C2 | — | 108 | 1 | no | — |
| 341 | C2 | — | 108 | 3 | no | — |
| 342 | C2 | #11722478 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D3×D9 |
| commutator, cosocle | C22×C3×C9 | C24 |
| Frattini | C22×C3 | C22×D32 |
| Fitting | C3×C42×C9 | C22 |
| socle | C22×C32 | C23×D3 |
| hypercenter | C42 | D3×D9 |
| hypocenter | C3×C9 | #560 |
| LCS | G ▷ C22×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11721711 | C2 | semidirect |
| 2. C9×#876 | C2 | semidirect |
| 3. C3×#63438 | C2 | semidirect |
| 4. #11721051 | C2 | semidirect |
| 5. #11721039 | C2 | semidirect |
| 6. #11721005 | C2 | semidirect |
| 7. #11720997 | C2 | semidirect |
| 12. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 15. C2×(C3⋊D9)⋊C4 | C22 | semidirect |
| 16. C3×C42×C9 | C22 | semidirect |
| 19. C9×Dic3⋊C4 | C22 | semidirect |
| 20. C3×Dic9⋊C4 | C22 | semidirect |
| 22. #88445 | C22 | semidirect |
| 35. #63438 | D3 | semidirect |
| 77. C42×C9 | C2×D3 | semidirect |
| 81. Dic9⋊C4 | C2×D3 | semidirect |
| 104. #876 | D9 | semidirect |
| 164. C3×C42 | C2×D9 | semidirect |
| 173. Dic3⋊C4 | C2×D9 | semidirect |
| 209. C3×C9 | #560 | semidirect |
| 266. C42 | D3×D9 | semidirect |
| 297. C9 | #5711 | semidirect |
| 336. C3 | #10589813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721711 | 2 |
| C9×#876 | 2 |
| C3×#63438 | 2 |
| #11721051 | 2 |
| #11721039 | 2 |
| #11721005 | 2 |
| #11720997 | 2 |
| #10594023 | 3 |
| #10589813 | 3 |