Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 3. #26021097 | C2 | semidirect |
| 5. #26018165 | C2 | semidirect |
| 6. #26018143 | C2 | semidirect |
| 7. C89×#1549 | C2 | semidirect |
| 144. D356 | #101 | semidirect |
| 187. #1549 | D89 | semidirect |
| 191. C89 | #9357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030061 | 2 |
| #26029373 | 2 |
| #26021097 | 2 |
| #26018689 | 2 |
| #26018165 | 2 |
| #26018143 | 2 |
| C89×#1549 | 2 |
| #9357 | 89 |