Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 15. #17988717 | C4 | semidirect |
| 17. Q8×#10596831 | C4 | semidirect |
| 19. #17988711 | C4 | semidirect |
| 24. #446×C73 | C4 | semidirect |
| 150. C73 | #8679 | semidirect |
| 154. #446 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625853 | 2 |
| #22625481 | 2 |
| #22625364 | 2 |
| #22624786 | 2 |
| #22618862 | 2 |
| #8679 | 73 |