Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
352 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26022049 | C2 | semidirect |
| 3. #26022006 | C2 | semidirect |
| 4. Q8⋊#13083549 | C2 | semidirect |
| 5. #26018208 | C2 | semidirect |
| 6. #26018206 | C2 | semidirect |
| 7. C89×Q8⋊C16 | C2 | semidirect |
| 105. Q8×C89 | M32 | semidirect |
| 117. D356 | M32 | semidirect |
| 162. Q8⋊C16 | D89 | semidirect |
| 165. C89 | #11623 | semidirect |
| 263. Q8 | #15667951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#13083575 | 2 |
| #26022049 | 2 |
| #26022006 | 2 |
| Q8⋊#13083549 | 2 |
| #26018208 | 2 |
| #26018206 | 2 |
| C89×Q8⋊C16 | 2 |
| #11623 | 89 |