Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26029829 | C2 | semidirect |
| 2. #26021988 | C2 | semidirect |
| 3. #26021862 | C2 | semidirect |
| 4. #26018354 | C2 | semidirect |
| 5. C89×#3414 | C2 | semidirect |
| 36. #15667944 | D4 | semidirect |
| 44. C2×Q16×C89 | D4 | semidirect |
| 46. C2×D8×C89 | D4 | semidirect |
| 52. C2×C16×C89 | D4 | semidirect |
| 143. #3414 | D89 | semidirect |
| 148. C89 | #13309 | semidirect |
| 170. C2×Q16 | C22⋊D89 | semidirect |
| 172. C2×D8 | C22⋊D89 | semidirect |
| 191. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029829 | 2 |
| #26021988 | 2 |
| #26021862 | 2 |
| #26018354 | 2 |
| C89×#3414 | 2 |
| #13309 | 89 |