Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 22. #17988983 | C4 | semidirect |
| 23. #17988939 | C4 | semidirect |
| 24. #17988938 | C4 | semidirect |
| 28. #500×C73 | C4 | semidirect |
| 165. C73 | #9280 | semidirect |
| 168. #500 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626836 | 2 |
| #22625323 | 2 |
| #22625294 | 2 |
| #22624788 | 2 |
| #22624754 | 2 |
| #22621091 | 2 |
| #9280 | 73 |