Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
630 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 630 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 |
|---|---|---|
| 2. #26021244 | C2 | semidirect |
| 5. #26018673 | C2 | semidirect |
| 6. #26018609 | C2 | semidirect |
| 7. C89×#1559 | C2 | semidirect |
| 238. #1559 | D89 | semidirect |
| 243. C89 | #8485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034862 | 2 |
| #26021244 | 2 |
| #26018860 | 2 |
| #26018715 | 2 |
| #26018673 | 2 |
| #26018609 | 2 |
| C89×#1559 | 2 |
| #8485 | 89 |