Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22583546 | C2 | semidirect |
| 5. #31826420 | C2 | semidirect |
| 6. #31826225 | C2 | semidirect |
| 7. #336×C283 | C2 | semidirect |
| 14. #22583535 | C4 | semidirect |
| 15. #22583535 | C4 | semidirect |
| 16. #22583532 | C4 | semidirect |
| 17. #22583532 | C4 | semidirect |
| 105. C283 | #1929 | semidirect |
| 113. #336 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583546 | 2 |
| C2×#22583538 | 2 |
| #31826462 | 2 |
| #31826431 | 2 |
| #31826420 | 2 |
| #31826225 | 2 |
| #336×C283 | 2 |
| #1929 | 283 |