Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
544 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 14. #17988453 | C4 | semidirect |
| 18. C4⋊C4×Dic73 | C4 | semidirect |
| 19. C4⋊C4×Dic73 | C4 | semidirect |
| 22. #382×C73 | C4 | semidirect |
| 191. C73 | #8714 | semidirect |
| 196. #382 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625823 | 2 |
| #22625107 | 2 |
| #22624804 | 2 |
| #22612324 | 2 |
| #8714 | 73 |