Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
310 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26018310 | C2 | semidirect |
| 5. #26018308 | C2 | semidirect |
| 6. #26018306 | C2 | semidirect |
| 7. C89×#1365 | C2 | semidirect |
| 129. #1365 | D89 | semidirect |
| 132. C89 | #11942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030763 | 2 |
| #26022006 | 2 |
| #335×D89 | 2 |
| #26018310 | 2 |
| #26018308 | 2 |
| #26018306 | 2 |
| C89×#1365 | 2 |
| #11942 | 89 |