Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
396 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 1. #22626836 | C2 | semidirect |
| 2. #22625404 | C2 | semidirect |
| 5. #22624788 | C2 | semidirect |
| 6. #22624756 | C2 | semidirect |
| 170. C73 | #9284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626836 | 2 |
| #22625404 | 2 |
| #22625402 | 2 |
| #22625292 | 2 |
| #22624788 | 2 |
| #22624756 | 2 |
| #22621068 | 2 |
| #9284 | 73 |