Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
432 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 432 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 |
|---|---|---|
| 24. #17988990 | C4 | semidirect |
| 25. #17988966 | C4 | semidirect |
| 26. #17988938 | C4 | semidirect |
| 30. #487×C73 | C4 | semidirect |
| 78. #11924038 | Q16 | semidirect |
| 187. C73 | #9056 | semidirect |
| 193. #487 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626727 | 2 |
| #22626107 | 2 |
| #22625315 | 2 |
| #22625240 | 2 |
| #22624766 | 2 |
| #22624763 | 2 |
| #22620516 | 2 |
| #9056 | 73 |