Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
490 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. C2×#19151397 | C2 | semidirect |
| 5. #26020246 | C2 | semidirect |
| 6. #101×Dic89 | C2 | semidirect |
| 7. C2×#356×C89 | C2 | semidirect |
| 231. C2×#356 | D89 | semidirect |
| 236. C89 | #13228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025229 | 2 |
| C2×#19151397 | 2 |
| C2×#19151394 | 2 |
| #26020246 | 2 |
| #101×Dic89 | 2 |
| C2×#356×C89 | 2 |
| #13228 | 89 |