Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1026 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. #26021051 | C2 | semidirect |
| 3. #26018948 | C2 | semidirect |
| 4. #26018864 | C2 | semidirect |
| 5. C89×#1466 | C2 | semidirect |
| 14. C2×C4⋊#10623494 | C22 | semidirect |
| 16. C2×#15667923 | C22 | semidirect |
| 21. #432×C89 | C22 | semidirect |
| 173. #1466 | D89 | semidirect |
| 174. C89 | #8456 | semidirect |
| 184. #432 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034016 | 2 |
| #26021051 | 2 |
| #26018948 | 2 |
| #26018864 | 2 |
| C89×#1466 | 2 |
| #8456 | 89 |