Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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×#22583643 | C2 | semidirect |
| 3. #31827041 | C2 | semidirect |
| 4. #31826945 | C2 | semidirect |
| 5. #31826688 | C2 | semidirect |
| 6. #31826681 | C2 | semidirect |
| 7. #31826676 | C2 | semidirect |
| 8. #31826671 | C2 | semidirect |
| 9. #31826467 | C2 | semidirect |
| 10. C2×#22583535 | C2 | semidirect |
| 11. #424×C283 | C2 | semidirect |
| 146. C283 | #3046 | semidirect |
| 156. #424 | 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×#22583632 | 2 |
| #31827041 | 2 |
| #31826945 | 2 |
| #31826688 | 2 |
| #31826681 | 2 |
| #31826676 | 2 |
| #31826671 | 2 |
| #31826467 | 2 |
| C2×#22583535 | 2 |
| #424×C283 | 2 |
| #3046 | 283 |