Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
482 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19151418 | C2 | semidirect |
| 3. C2×#19151414 | C2 | semidirect |
| 6. #26020133 | C2 | semidirect |
| 7. C89×#2141 | C2 | semidirect |
| 13. #19151983 | C4 | semidirect |
| 170. #2141 | D89 | semidirect |
| 173. C89 | #13260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151983 | 2 |
| C2×#19151418 | 2 |
| C2×#19151414 | 2 |
| C2×#19151412 | 2 |
| #26021967 | 2 |
| #26020133 | 2 |
| C89×#2141 | 2 |
| #13260 | 89 |