Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22583630 | C2 | semidirect |
| 2. C2×#22583617 | C2 | semidirect |
| 3. #31827043 | C2 | semidirect |
| 4. #31826721 | C2 | semidirect |
| 5. #31826716 | C2 | semidirect |
| 6. #31826696 | C2 | semidirect |
| 7. #31826692 | C2 | semidirect |
| 8. C2×#22583541 | C2 | semidirect |
| 9. #31826466 | C2 | semidirect |
| 10. #31826464 | C2 | semidirect |
| 11. #537×C283 | C2 | semidirect |
| 58. C2×C283⋊C8 | D4 | semidirect |
| 152. C283 | #3060 | semidirect |
| 157. #537 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583630 | 2 |
| C2×#22583617 | 2 |
| #31827043 | 2 |
| #31826721 | 2 |
| #31826716 | 2 |
| #31826696 | 2 |
| #31826692 | 2 |
| C2×#22583541 | 2 |
| #31826466 | 2 |
| #31826464 | 2 |
| #537×C283 | 2 |
| #3060 | 283 |