Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
536 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 25. #17988873 | C4 | semidirect |
| 26. #17988872 | C4 | semidirect |
| 27. #17988794 | C4 | semidirect |
| 32. #462×C73 | C4 | semidirect |
| 213. C73 | #9324 | semidirect |
| 221. #462 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626371 | 2 |
| #22626107 | 2 |
| #22625323 | 2 |
| #22625274 | 2 |
| #22624818 | 2 |
| #22624783 | 2 |
| #22620060 | 2 |
| #9324 | 73 |