Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19151414 | C2 | semidirect |
| 5. #26021168 | C2 | semidirect |
| 6. #26018340 | C2 | semidirect |
| 7. C22×Q32×C89 | C2 | semidirect |
| 197. C22×Q32 | D89 | semidirect |
| 203. C89 | #13339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| #26030741 | 2 |
| C2×#19151414 | 2 |
| C2×#19151406 | 2 |
| #26021168 | 2 |
| #26018340 | 2 |
| C22×Q32×C89 | 2 |
| #13339 | 89 |