Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26027155 | C2 | semidirect |
| 4. #26018253 | C2 | semidirect |
| 5. #26018252 | C2 | semidirect |
| 6. #26018199 | C2 | semidirect |
| 205. C89 | #12150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027155 | 2 |
| #26021500 | 2 |
| #26019238 | 2 |
| #26018253 | 2 |
| #26018252 | 2 |
| #26018199 | 2 |
| C89×#1607 | 2 |
| #12150 | 89 |