Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #26020389 | C2 | semidirect |
| 5. #26018143 | C2 | semidirect |
| 6. #26018088 | C2 | semidirect |
| 7. C89×#1574 | C2 | semidirect |
| 169. #1574 | D89 | semidirect |
| 174. C89 | #8900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029373 | 2 |
| #26020389 | 2 |
| #26018689 | 2 |
| #26018632 | 2 |
| #26018143 | 2 |
| #26018088 | 2 |
| C89×#1574 | 2 |
| #8900 | 89 |