Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 117 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×#19151402 | C2 | semidirect |
| 5. #26021114 | C2 | semidirect |
| 6. #26018329 | C2 | semidirect |
| 7. C22×Q32×C89 | C2 | semidirect |
| 192. C22×Q32 | D89 | semidirect |
| 199. C89 | #13329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667955 | 2 |
| C2×#19151983 | 2 |
| C2×#19151402 | 2 |
| C2×#19151400 | 2 |
| #26021114 | 2 |
| #26018329 | 2 |
| C22×Q32×C89 | 2 |
| #13329 | 89 |