Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 14. C2×#15667944 | C4 | semidirect |
| 15. C2×#15667937 | C4 | semidirect |
| 221. C89 | #9256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151929 | 2 |
| #26023123 | 2 |
| #26021236 | 2 |
| #26020336 | 2 |
| #26018823 | 2 |
| #26018099 | 2 |
| C89×#1289 | 2 |
| #9256 | 89 |