Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. #26021947 | C2 | semidirect |
| 3. #26020805 | C2 | semidirect |
| 5. #26020471 | C2 | semidirect |
| 6. #26018375 | C2 | semidirect |
| 200. C89 | #13430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021947 | 2 |
| #26021944 | 2 |
| #26020805 | 2 |
| #26020800 | 2 |
| #26020471 | 2 |
| #26018375 | 2 |
| C89×#3200 | 2 |
| #13430 | 89 |