Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
436 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 6. C2×#15668004 | C4 | semidirect |
| 8. #19151537 | C4 | semidirect |
| 10. #19151528 | C4 | semidirect |
| 16. #19151444 | C4 | semidirect |
| 178. C89 | #11760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025950 | 2 |
| #26019985 | 2 |
| #26018277 | 2 |
| #26018253 | 2 |
| C89×#1464 | 2 |
| #11760 | 89 |