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. #26018311 | C2 | semidirect |
| 5. #26018310 | C2 | semidirect |
| 6. #26018309 | C2 | semidirect |
| 7. C89×#1365 | C2 | semidirect |
| 132. #1365 | D89 | semidirect |
| 133. C89 | #11941 | 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 |
| #26018311 | 2 |
| #26018310 | 2 |
| #26018309 | 2 |
| C89×#1365 | 2 |
| #11941 | 89 |