Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26021503 | C2 | semidirect |
| 2. #26019203 | C2 | semidirect |
| 4. #26018273 | C2 | semidirect |
| 5. #26018249 | C2 | semidirect |
| 6. #26018200 | C2 | semidirect |
| 7. C89×#2824 | C2 | semidirect |
| 218. #2824 | D89 | semidirect |
| 225. C89 | #12136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021503 | 2 |
| #26019203 | 2 |
| #26019169 | 2 |
| #26018273 | 2 |
| #26018249 | 2 |
| #26018200 | 2 |
| C89×#2824 | 2 |
| #12136 | 89 |