Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022394 | C2 | semidirect |
| 4. #26018322 | C2 | semidirect |
| 5. #26018308 | C2 | semidirect |
| 7. C89×#1591 | C2 | semidirect |
| 91. C8×C89 | SD32 | semidirect |
| 114. #1591 | D89 | semidirect |
| 118. C89 | #12484 | semidirect |
| 202. C8 | #15667955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022394 | 2 |
| #26022292 | 2 |
| #26019844 | 2 |
| #26018322 | 2 |
| #26018308 | 2 |
| #26018297 | 2 |
| C89×#1591 | 2 |
| #12484 | 89 |