Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
394 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26021097 | C2 | semidirect |
| 2. #26019040 | C2 | semidirect |
| 4. #26018933 | C2 | semidirect |
| 6. #26018143 | C2 | semidirect |
| 166. C89 | #10489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021097 | 2 |
| #26019040 | 2 |
| #26018987 | 2 |
| #26018933 | 2 |
| #26018669 | 2 |
| #26018143 | 2 |
| C89×#3206 | 2 |
| #10489 | 89 |