Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
156 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26018316 | C2 | semidirect |
| 3. C89×#1312 | C2 | semidirect |
| 26. D712 | C16 | semidirect |
| 72. #1312 | D89 | semidirect |
| 73. C89 | #7070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D712 | 2 |
| #26018316 | 2 |
| C89×#1312 | 2 |
| #7070 | 89 |