Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26022525 | C2 | semidirect |
| 4. #26018308 | C2 | semidirect |
| 5. Q8⋊#13083549 | C2 | semidirect |
| 7. C89×#1674 | C2 | semidirect |
| 60. D712 | Q16 | semidirect |
| 130. #1674 | D89 | semidirect |
| 134. C89 | #12404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D712 | 2 |
| #26022525 | 2 |
| #26022386 | 2 |
| #26018308 | 2 |
| Q8⋊#13083549 | 2 |
| #26018212 | 2 |
| C89×#1674 | 2 |
| #12404 | 89 |