Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 26. #15667923 | Q8 | semidirect |
| 41. #97×C89 | Q8 | semidirect |
| 119. C89 | #10584 | semidirect |
| 150. #97 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028524 | 2 |
| #26020387 | 2 |
| #26018134 | 2 |
| #26018133 | 2 |
| C89×#1847 | 2 |
| #10584 | 89 |