Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31827013 | C2 | semidirect |
| 2. C4×#17985393 | C2 | semidirect |
| 3. #31826787 | C2 | semidirect |
| 4. #31826750 | C2 | semidirect |
| 5. #31826746 | C2 | semidirect |
| 6. #31826657 | C2 | semidirect |
| 7. #31826609 | C2 | semidirect |
| 8. #31826574 | C2 | semidirect |
| 9. #31826566 | C2 | semidirect |
| 10. #31826521 | C2 | semidirect |
| 11. #460×C283 | C2 | semidirect |
| 88. D1132 | #41 | semidirect |
| 106. Q8×C283 | #41 | semidirect |
| 144. C283 | #3115 | semidirect |
| 151. #460 | D283 | semidirect |
| 233. Q8 | #17985391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827013 | 2 |
| C4×#17985393 | 2 |
| #31826787 | 2 |
| #31826750 | 2 |
| #31826746 | 2 |
| #31826657 | 2 |
| #31826609 | 2 |
| #31826574 | 2 |
| #31826566 | 2 |
| #31826521 | 2 |
| #460×C283 | 2 |
| #3115 | 283 |