Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22583643 | C2 | semidirect |
| 3. #31827036 | C2 | semidirect |
| 4. #31826946 | C2 | semidirect |
| 5. #31826686 | C2 | semidirect |
| 6. #31826679 | C2 | semidirect |
| 7. #31826674 | C2 | semidirect |
| 8. #31826669 | C2 | semidirect |
| 9. #31826493 | C2 | semidirect |
| 10. C2×#22583533 | C2 | semidirect |
| 11. #417×C283 | C2 | semidirect |
| 146. C283 | #3046 | semidirect |
| 157. #417 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583643 | 2 |
| C2×#22583630 | 2 |
| #31827036 | 2 |
| #31826946 | 2 |
| #31826686 | 2 |
| #31826679 | 2 |
| #31826674 | 2 |
| #31826669 | 2 |
| #31826493 | 2 |
| C2×#22583533 | 2 |
| #417×C283 | 2 |
| #3046 | 283 |