Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
740 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #26020340 | C2 | semidirect |
| 4. #26018130 | C2 | semidirect |
| 11. #19151534 | C4 | semidirect |
| 173. C89 | #9024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151534 | 2 |
| #26020340 | 2 |
| C2×#19151322 | 2 |
| #26018130 | 2 |
| C89×#2312 | 2 |
| #9024 | 89 |