Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 167 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. #26022477 | C2 | semidirect |
| 3. #26022396 | C2 | semidirect |
| 4. #26022292 | C2 | semidirect |
| 5. Q8×#13083549 | C2 | semidirect |
| 6. C4×#15667955 | C2 | semidirect |
| 7. Q8×Q16×C89 | C2 | semidirect |
| 62. Q16×C89 | #41 | semidirect |
| 75. Q8×C89 | SD32 | semidirect |
| 107. Q8×Q16 | D89 | semidirect |
| 113. C89 | #33929 | semidirect |
| 161. Q16 | #13083575 | semidirect |
| 181. Q8 | #15667955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033227 | 2 |
| #26022477 | 2 |
| #26022396 | 2 |
| #26022292 | 2 |
| Q8×#13083549 | 2 |
| C4×#15667955 | 2 |
| Q8×Q16×C89 | 2 |
| #33929 | 89 |