Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
728 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 728 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 |
|---|---|---|
| 2. #26021229 | C2 | semidirect |
| 4. #26018990 | C2 | semidirect |
| 5. #26018989 | C2 | semidirect |
| 7. C89×#1994 | C2 | semidirect |
| 8. #19152352 | C4 | semidirect |
| 228. #1994 | D89 | semidirect |
| 233. C89 | #8531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034663 | 2 |
| #26021229 | 2 |
| #26021080 | 2 |
| #26018990 | 2 |
| #26018989 | 2 |
| #26018985 | 2 |
| C89×#1994 | 2 |
| #8531 | 89 |