Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26018698 | C2 | semidirect |
| 5. #26018595 | C2 | semidirect |
| 6. #26018125 | C2 | semidirect |
| 7. C89×#1308 | C2 | semidirect |
| 200. #1308 | D89 | semidirect |
| 202. C89 | #9531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030425 | 2 |
| #26029232 | 2 |
| #26018884 | 2 |
| #26018698 | 2 |
| #26018595 | 2 |
| #26018125 | 2 |
| C89×#1308 | 2 |
| #9531 | 89 |