Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #26018308 | C2 | semidirect |
| 5. #26018307 | C2 | semidirect |
| 6. #26018306 | C2 | semidirect |
| 7. C89×#1364 | C2 | semidirect |
| 135. #1364 | D89 | semidirect |
| 136. C89 | #11940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D89 | 2 |
| #26022006 | 2 |
| #26018999 | 2 |
| #26018308 | 2 |
| #26018307 | 2 |
| #26018306 | 2 |
| C89×#1364 | 2 |
| #11940 | 89 |