Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
494 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 494 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×Dic356 | C2 | semidirect |
| 2. #26022532 | C2 | semidirect |
| 4. #26022391 | C2 | semidirect |
| 5. Q8×#13083549 | C2 | semidirect |
| 29. #15667956 | Q8 | direct (N × H) |
| 49. Dic356 | C2×Q8 | semidirect |
| 55. #13083549 | C2×Q8 | semidirect |
| 72. Q8×C89 | SD32 | semidirect |
| 111. C89 | Q8×SD32 | semidirect |
| 179. Q8 | #15667956 | 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 |
| #26022532 | 2 |
| #26022399 | 2 |
| #26022391 | 2 |
| Q8×#13083549 | 2 |
| C4×#15667956 | 2 |
| Q8×D8×C89 | 2 |
| Q8×SD32 | 89 |