Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
516 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626584 | C2 | semidirect |
| 2. #22626252 | C2 | semidirect |
| 3. #22626165 | C2 | semidirect |
| 4. #22624998 | C2 | semidirect |
| 17. #17988846 | C4 | semidirect |
| 18. #17988845 | C4 | semidirect |
| 19. #17988837 | C4 | semidirect |
| 24. #469×C73 | C4 | semidirect |
| 38. #14556659 | D4 | semidirect |
| 43. C2×Dic292 | C2×C4 | semidirect |
| 61. #14556523 | C2×C4 | semidirect |
| 65. C2×D8×C73 | C2×C4 | semidirect |
| 68. #106×C73 | C2×C4 | semidirect |
| 204. C73 | #13008 | semidirect |
| 213. #469 | #64408 | semidirect |
| 230. C2×D8 | C2×#64408 | semidirect |
| 264. #106 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626584 | 2 |
| #22626252 | 2 |
| #22626165 | 2 |
| #22624998 | 2 |
| #22619538 | 2 |
| #13008 | 73 |