Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26018252 | C2 | semidirect |
| 5. #26018252 | C2 | semidirect |
| 6. #26018200 | C2 | semidirect |
| 7. C89×#2722 | C2 | semidirect |
| 198. #2722 | D89 | semidirect |
| 205. C89 | #12150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021503 | 2 |
| #26019237 | 2 |
| #26018252 | 2 |
| #26018200 | 2 |
| C89×#2722 | 2 |
| #12150 | 89 |