Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26033388 | C2 | semidirect |
| 2. #26030698 | C2 | semidirect |
| 3. #26021981 | C2 | semidirect |
| 4. #26021145 | C2 | semidirect |
| 5. C89×#1375 | C2 | semidirect |
| 35. C2×Dic356 | D4 | semidirect |
| 41. C2×D712 | D4 | semidirect |
| 60. C2×C16×C89 | D4 | semidirect |
| 168. #1375 | D89 | semidirect |
| 169. C89 | #13340 | semidirect |
| 221. C2×C16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033388 | 2 |
| #26030698 | 2 |
| #26021981 | 2 |
| #26021145 | 2 |
| C89×#1375 | 2 |
| #13340 | 89 |