Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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. #26022525 | C2 | semidirect |
| 3. #26022389 | C2 | semidirect |
| 4. #26022386 | C2 | semidirect |
| 5. Q8×#13083549 | C2 | semidirect |
| 7. Q8×D8×C89 | C2 | semidirect |
| 29. #15667953 | Q8 | direct (N × H) |
| 51. D712 | C2×Q8 | semidirect |
| 56. #13083549 | C2×Q8 | semidirect |
| 63. D8×C89 | C2×Q8 | semidirect |
| 74. Q8×C89 | D16 | semidirect |
| 110. Q8×D8 | D89 | semidirect |
| 116. C89 | Q8×D16 | semidirect |
| 167. D8 | Q8×D89 | semidirect |
| 184. Q8 | #15667953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D712 | 2 |
| #26022525 | 2 |
| #26022389 | 2 |
| #26022386 | 2 |
| Q8×#13083549 | 2 |
| C4×#15667953 | 2 |
| Q8×D8×C89 | 2 |
| Q8×D16 | 89 |