Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
656 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 3. #31826361 | C2 | semidirect |
| 5. C4×Dic283⋊C4 | C2 | semidirect |
| 8. #22583569 | C4 | semidirect |
| 26. C4⋊Dic283 | C2×C4 | semidirect |
| 31. C4×Dic283 | C2×C4 | semidirect |
| 55. C2×C4×C283 | C4⋊C4 | semidirect |
| 80. C283 | #2296 | semidirect |
| 136. C2×C4 | Dic283⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583569 | 2 |
| C22×C4×Dic283 | 2 |
| #31826361 | 2 |
| #31826337 | 2 |
| C4×Dic283⋊C4 | 2 |
| C2×#117×C283 | 2 |
| #2296 | 283 |