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×#19151413 | C2 | semidirect |
| 4. #26021973 | C2 | semidirect |
| 6. #26020134 | C2 | semidirect |
| 13. #19151981 | C4 | 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×#19151981 | 2 |
| C2×#19151418 | 2 |
| C2×#19151413 | 2 |
| #26021973 | 2 |
| #26021968 | 2 |
| #26020134 | 2 |
| C2×#361×C89 | 2 |
| #13260 | 89 |