Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
270 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 16. #19151320 | C4 | semidirect |
| 17. #19151319 | C4 | semidirect |
| 132. C89 | #8795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020414 | 2 |
| #26020389 | 2 |
| #26018545 | 2 |
| #26018112 | 2 |
| #26018111 | 2 |
| #26018110 | 2 |
| C89×#1286 | 2 |
| #8795 | 89 |