Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
524 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 12. C2×#15667945 | C4 | semidirect |
| 13. C2×#15667936 | C4 | semidirect |
| 212. C89 | #9257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151931 | 2 |
| #26023131 | 2 |
| #26021238 | 2 |
| #26020343 | 2 |
| #26018119 | 2 |
| #26018098 | 2 |
| C89×#1520 | 2 |
| #9257 | 89 |