Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22601474 | C2 | semidirect |
| 2. C2×#17986434 | C2 | semidirect |
| 3. #22598826 | C2 | semidirect |
| 4. #22590075 | C2 | semidirect |
| 5. #22590055 | C2 | semidirect |
| 6. #22586426 | C2 | semidirect |
| 7. C71×#1976 | C2 | semidirect |
| 65. #14556068 | D4 | semidirect |
| 67. C2×C71⋊C16 | D4 | semidirect |
| 73. C2×Q16×C71 | D4 | semidirect |
| 75. C2×D8×C71 | D4 | semidirect |
| 223. #1976 | D71 | semidirect |
| 225. C71 | #13334 | semidirect |
| 265. C2×Q16 | D284 | semidirect |
| 277. C2×D8 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| C2×#17986434 | 2 |
| #22598826 | 2 |
| #22590075 | 2 |
| #22590055 | 2 |
| #22586426 | 2 |
| C71×#1976 | 2 |
| #13334 | 71 |