Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 42. #15667923 | Q8 | semidirect |
| 58. #97×C89 | Q8 | semidirect |
| 59. #97×C89 | Q8 | semidirect |
| 174. C89 | #10584 | semidirect |
| 217. #97 | Dic178 | semidirect |
| 218. #97 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028524 | 2 |
| #26020420 | 2 |
| #26020386 | 2 |
| #26020385 | 2 |
| #26018134 | 2 |
| C89×#1295 | 2 |
| #10584 | 89 |