Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
328 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26019043 | C2 | semidirect |
| 2. #26019041 | C2 | semidirect |
| 3. #26019040 | C2 | semidirect |
| 6. #26018165 | C2 | semidirect |
| 153. C89 | #10612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019043 | 2 |
| #26019041 | 2 |
| #26019040 | 2 |
| #26018920 | 2 |
| #26018165 | 2 |
| C89×#1545 | 2 |
| #10612 | 89 |