Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 29. #15667958 | Q8 | direct (N × H) |
| 72. Q8×C89 | Q32 | semidirect |
| 106. C89 | Q8×Q32 | semidirect |
| 174. Q8 | #15667958 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic356 | 2 |
| #26022525 | 2 |
| #26022404 | 2 |
| #26022401 | 2 |
| Q8×#13083549 | 2 |
| C4×#15667958 | 2 |
| Q8×Q16×C89 | 2 |
| Q8×Q32 | 89 |