Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
656 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 96 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. #22625436 | C2 | semidirect |
| 2. #22625422 | C2 | semidirect |
| 5. #22625205 | C2 | semidirect |
| 6. #22625204 | C2 | semidirect |
| 264. C73 | #8478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625436 | 2 |
| #22625422 | 2 |
| #22625264 | 2 |
| #22625205 | 2 |
| #22625204 | 2 |
| #22623754 | 2 |
| #8478 | 73 |