Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#19152029 | C2 | semidirect |
| 2. #26030681 | C2 | semidirect |
| 3. #26030679 | C2 | semidirect |
| 4. #26022512 | C2 | semidirect |
| 5. #26022508 | C2 | semidirect |
| 6. #26022504 | C2 | semidirect |
| 7. #26022501 | C2 | semidirect |
| 8. C4×C16×D89 | C2 | semidirect |
| 9. C89×#2248 | C2 | semidirect |
| 65. C16×D89 | D4 | semidirect |
| 159. C4×C89 | #508 | semidirect |
| 176. #2248 | D89 | semidirect |
| 180. C89 | #33713 | semidirect |
| 333. C4 | #19152029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152029 | 2 |
| #26030681 | 2 |
| #26030679 | 2 |
| #26022512 | 2 |
| #26022508 | 2 |
| #26022504 | 2 |
| #26022501 | 2 |
| C4×C16×D89 | 2 |
| C89×#2248 | 2 |
| #33713 | 89 |