Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 2. #26019043 | C2 | semidirect |
| 5. #26018141 | C2 | semidirect |
| 6. #26018089 | C2 | semidirect |
| 7. C89×#1837 | C2 | semidirect |
| 168. #1837 | D89 | semidirect |
| 174. C89 | #8901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029382 | 2 |
| #26019043 | 2 |
| #26018689 | 2 |
| #26018635 | 2 |
| #26018141 | 2 |
| #26018089 | 2 |
| C89×#1837 | 2 |
| #8901 | 89 |