Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
782 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 159 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. #26020248 | C2 | semidirect |
| 2. #26018937 | C2 | semidirect |
| 4. #26018576 | C2 | semidirect |
| 112. D4×C89 | #101 | semidirect |
| 168. C89 | #8398 | semidirect |
| 275. D4 | #15667931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020248 | 2 |
| #26018937 | 2 |
| #26018677 | 2 |
| #26018576 | 2 |
| C2×#554×C89 | 2 |
| #8398 | 89 |