Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
920 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26031263 | C2 | semidirect |
| 2. #26030774 | C2 | semidirect |
| 3. #26019569 | C2 | semidirect |
| 4. #26018890 | C2 | semidirect |
| 5. #26018863 | C2 | semidirect |
| 156. C89 | #19065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031263 | 2 |
| #26030774 | 2 |
| #26019569 | 2 |
| #26018890 | 2 |
| #26018863 | 2 |
| C89×#3548 | 2 |
| #19065 | 89 |