Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22583631 | C2 | semidirect |
| 2. #31827137 | C2 | semidirect |
| 3. #31827135 | C2 | semidirect |
| 4. #31826841 | C2 | semidirect |
| 5. #31826700 | C2 | semidirect |
| 6. #31826666 | C2 | semidirect |
| 7. #31826611 | C2 | semidirect |
| 8. #31826609 | C2 | semidirect |
| 9. C4×#17985382 | C2 | semidirect |
| 10. #31826530 | C2 | semidirect |
| 11. #460×C283 | C2 | semidirect |
| 58. #17985382 | D4 | semidirect |
| 130. C4×C283 | #135 | semidirect |
| 142. C283 | #3287 | semidirect |
| 150. #460 | D283 | semidirect |
| 276. C4 | #22583631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583631 | 2 |
| #31827137 | 2 |
| #31827135 | 2 |
| #31826841 | 2 |
| #31826700 | 2 |
| #31826666 | 2 |
| #31826611 | 2 |
| #31826609 | 2 |
| C4×#17985382 | 2 |
| #31826530 | 2 |
| #460×C283 | 2 |
| #3287 | 283 |