Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 4. #26018310 | C2 | semidirect |
| 5. Q8⋊#13083549 | C2 | semidirect |
| 6. #26018216 | C2 | semidirect |
| 7. Q8×Q16×C89 | C2 | semidirect |
| 68. Q16×C89 | SD16 | semidirect |
| 90. Q8×C89 | SD32 | semidirect |
| 128. Q8×Q16 | D89 | semidirect |
| 135. C89 | #12354 | semidirect |
| 189. Q16 | #13083561 | semidirect |
| 218. Q8 | #15667955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022477 | 2 |
| #26022292 | 2 |
| #26019612 | 2 |
| #26018310 | 2 |
| Q8⋊#13083549 | 2 |
| #26018216 | 2 |
| Q8×Q16×C89 | 2 |
| #12354 | 89 |