Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
708 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 9. C22×Dic356 | C4 | semidirect |
| 15. C2×#15667937 | C4 | semidirect |
| 115. C22⋊Dic89 | Q16 | semidirect |
| 235. C89 | #9258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151756 | 2 |
| #26023084 | 2 |
| #26021236 | 2 |
| #26020186 | 2 |
| #26018823 | 2 |
| #26018099 | 2 |
| C89×#1289 | 2 |
| #9258 | 89 |