Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26018087 | C2 | semidirect |
| 3. C89×#1374 | C2 | semidirect |
| 15. C2×D712 | C8 | semidirect |
| 129. #1374 | D89 | semidirect |
| 131. C89 | #7112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021118 | 2 |
| #26018087 | 2 |
| C89×#1374 | 2 |
| #7112 | 89 |