Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26022477 | C2 | semidirect |
| 3. #26019612 | C2 | semidirect |
| 4. #26018307 | C2 | semidirect |
| 5. Q8⋊#13083549 | C2 | semidirect |
| 6. #26018213 | C2 | semidirect |
| 7. Q8×D8×C89 | C2 | semidirect |
| 72. D8×C89 | SD16 | semidirect |
| 92. Q8×C89 | D16 | semidirect |
| 137. Q8×D8 | D89 | semidirect |
| 144. C89 | #12352 | semidirect |
| 206. D8 | #13083561 | semidirect |
| 229. Q8 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022477 | 2 |
| #26022287 | 2 |
| #26019612 | 2 |
| #26018307 | 2 |
| Q8⋊#13083549 | 2 |
| #26018213 | 2 |
| Q8×D8×C89 | 2 |
| #12352 | 89 |