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 |
|---|---|---|
| 3. #26019849 | C2 | semidirect |
| 5. #26018309 | C2 | semidirect |
| 6. #26018302 | C2 | semidirect |
| 7. C89×#1367 | C2 | semidirect |
| 87. C8×C89 | SD32 | semidirect |
| 112. #1367 | D89 | semidirect |
| 115. C89 | #12420 | semidirect |
| 196. C8 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022400 | 2 |
| #26022298 | 2 |
| #26019849 | 2 |
| C8×D712 | 2 |
| #26018309 | 2 |
| #26018302 | 2 |
| C89×#1367 | 2 |
| #12420 | 89 |