Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 33. C2×#13083549 | Q8 | semidirect |
| 38. #15667944 | Q8 | semidirect |
| 48. C2×C16×C89 | Q8 | semidirect |
| 127. C89 | #13459 | semidirect |
| 159. C2×C16 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030775 | 2 |
| #26022026 | 2 |
| #26021003 | 2 |
| #26018354 | 2 |
| #26018353 | 2 |
| #26018331 | 2 |
| C89×#2155 | 2 |
| #13459 | 89 |