Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
730 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26019946 | C2 | semidirect |
| 2. #26018078 | C2 | semidirect |
| 3. #26018073 | C2 | semidirect |
| 55. C2×Q8×C89 | M16 | semidirect |
| 62. C2×D4×C89 | M16 | semidirect |
| 170. C89 | #7631 | semidirect |
| 217. C2×Q8 | #13083558 | semidirect |
| 224. C2×D4 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019946 | 2 |
| #26018078 | 2 |
| #26018073 | 2 |
| C89×#2297 | 2 |
| #7631 | 89 |