Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. C2×C22⋊(C283⋊C8) | C2 | semidirect |
| 2. C4×C22⋊Dic283 | C2 | semidirect |
| 3. #31826202 | C2 | semidirect |
| 4. #31826199 | C2 | semidirect |
| 12. C2×#41×C283 | C4 | semidirect |
| 15. C22⋊Q8×C283 | C4 | semidirect |
| 17. #121×C283 | C4 | semidirect |
| 22. #117×C283 | C4 | semidirect |
| 112. C283 | #1501 | semidirect |
| 119. C2×#41 | Dic283 | semidirect |
| 123. C22⋊Q8 | Dic283 | semidirect |
| 125. #121 | Dic283 | semidirect |
| 130. #117 | Dic283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C283⋊C8) | 2 |
| C4×C22⋊Dic283 | 2 |
| #31826202 | 2 |
| #31826199 | 2 |
| #525×C283 | 2 |
| #1501 | 283 |