Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26020343 | C2 | semidirect |
| 4. #26018120 | C2 | semidirect |
| 8. #19151537 | C4 | semidirect |
| 9. #19151534 | C4 | semidirect |
| 176. C89 | #9469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024569 | 2 |
| #26020343 | 2 |
| #26020240 | 2 |
| #26018120 | 2 |
| C89×#2972 | 2 |
| #9469 | 89 |