Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 77 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. #26021209 | C2 | semidirect |
| 3. #26019038 | C2 | semidirect |
| 6. #26018609 | C2 | semidirect |
| 7. C89×#1285 | C2 | semidirect |
| 176. #1285 | D89 | semidirect |
| 177. C89 | #10509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031444 | 2 |
| #26021209 | 2 |
| #26019038 | 2 |
| #26018948 | 2 |
| #26018746 | 2 |
| #26018609 | 2 |
| C89×#1285 | 2 |
| #10509 | 89 |