Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
550 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #26030600 | C2 | semidirect |
| 3. #26021051 | C2 | semidirect |
| 4. #26018655 | C2 | semidirect |
| 5. #26018652 | C2 | semidirect |
| 6. #26018082 | C2 | semidirect |
| 7. C89×#3101 | C2 | semidirect |
| 207. #3101 | D89 | semidirect |
| 213. C89 | #10033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030600 | 2 |
| #26030252 | 2 |
| #26021051 | 2 |
| #26018655 | 2 |
| #26018652 | 2 |
| #26018082 | 2 |
| C89×#3101 | 2 |
| #10033 | 89 |