Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 11. #19151934 | C4 | semidirect |
| 14. #19151756 | C4 | semidirect |
| 109. C22⋊Dic89 | Q16 | semidirect |
| 232. C89 | #9276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031027 | 2 |
| #26023332 | 2 |
| #26021236 | 2 |
| #26018823 | 2 |
| C2×#19151334 | 2 |
| #26018098 | 2 |
| C89×#1294 | 2 |
| #9276 | 89 |