Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
510 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 510 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 |
|---|---|---|
| 8. C22×#13083564 | C4 | semidirect |
| 15. C2×#15667945 | C4 | semidirect |
| 17. C2×#15667936 | C4 | semidirect |
| 18. C2×#15667935 | C4 | semidirect |
| 227. C89 | #9784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151837 | 2 |
| #26021237 | 2 |
| #26020275 | 2 |
| #26020030 | 2 |
| #26018824 | 2 |
| #26018823 | 2 |
| C89×#1996 | 2 |
| #9784 | 89 |