Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #26029337 | C2 | semidirect |
| 5. #26018149 | C2 | semidirect |
| 6. #26018110 | C2 | semidirect |
| 7. C89×#1805 | C2 | semidirect |
| 11. #19151808 | C4 | semidirect |
| 12. #19151798 | C4 | semidirect |
| 186. #1805 | D89 | semidirect |
| 191. C89 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029724 | 2 |
| #26029337 | 2 |
| #26018811 | 2 |
| #26018650 | 2 |
| #26018149 | 2 |
| #26018110 | 2 |
| C89×#1805 | 2 |
| #9310 | 89 |