Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
378 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626267 | C2 | semidirect |
| 4. #22625851 | C2 | semidirect |
| 5. #22625008 | C2 | semidirect |
| 6. #22624994 | C2 | semidirect |
| 22. #17988710 | C4 | semidirect |
| 23. #17988709 | C4 | semidirect |
| 24. #17988708 | C4 | semidirect |
| 30. #444×C73 | C4 | semidirect |
| 196. C73 | #12830 | semidirect |
| 204. #444 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626267 | 2 |
| #22626251 | 2 |
| D73⋊#359 | 2 |
| #22625851 | 2 |
| #22625008 | 2 |
| #22624994 | 2 |
| #22618845 | 2 |
| #12830 | 73 |