Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26021946 | C2 | semidirect |
| 4. #26020802 | C2 | semidirect |
| 6. #26020471 | C2 | semidirect |
| 7. C89×#1392 | C2 | semidirect |
| 199. #1392 | D89 | semidirect |
| 200. C89 | #13430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031125 | 2 |
| #26021946 | 2 |
| #26021943 | 2 |
| #26020802 | 2 |
| #26020797 | 2 |
| #26020471 | 2 |
| C89×#1392 | 2 |
| #13430 | 89 |