Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 1. Q8×D712 | C2 | semidirect |
| 2. #26022476 | C2 | semidirect |
| 4. #26019612 | C2 | semidirect |
| 5. #26018306 | C2 | semidirect |
| 6. #26018214 | C2 | semidirect |
| 7. C89×Q8⋊C16 | C2 | semidirect |
| 68. D712 | SD16 | semidirect |
| 89. Q8×C89 | D16 | semidirect |
| 142. Q8⋊C16 | D89 | semidirect |
| 144. C89 | #12352 | semidirect |
| 229. Q8 | D1424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D712 | 2 |
| #26022476 | 2 |
| #26022288 | 2 |
| #26019612 | 2 |
| #26018306 | 2 |
| #26018214 | 2 |
| C89×Q8⋊C16 | 2 |
| #12352 | 89 |