Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
380 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26022046 | C2 | semidirect |
| 5. #26018345 | C2 | semidirect |
| 6. #26018341 | C2 | semidirect |
| 7. C89×#1953 | C2 | semidirect |
| 17. #19151413 | C4 | semidirect |
| 18. #19151410 | C4 | semidirect |
| 146. #1953 | D89 | semidirect |
| 149. C89 | #12942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029170 | 2 |
| #26022046 | 2 |
| #26021999 | 2 |
| C2×#19151404 | 2 |
| #26018345 | 2 |
| #26018341 | 2 |
| C89×#1953 | 2 |
| #12942 | 89 |