Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
914 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26025251 | C2 | semidirect |
| 2. #26021563 | C2 | semidirect |
| 3. #26021325 | C2 | semidirect |
| 4. #26021128 | C2 | semidirect |
| 5. #26020880 | C2 | semidirect |
| 6. C89×#1985 | C2 | semidirect |
| 158. #1985 | D89 | semidirect |
| 161. C89 | #32681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025251 | 2 |
| #26021563 | 2 |
| #26021325 | 2 |
| #26021128 | 2 |
| #26020880 | 2 |
| C89×#1985 | 2 |
| #32681 | 89 |