Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #31827184 | C2 | semidirect |
| 2. #31826856 | C2 | semidirect |
| 3. #31826684 | C2 | semidirect |
| 5. #31826673 | C2 | semidirect |
| 6. #31826595 | C2 | semidirect |
| 7. #31826566 | C2 | semidirect |
| 8. C4×Dic1132 | C2 | semidirect |
| 102. C283 | #3402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827184 | 2 |
| #31826856 | 2 |
| #31826684 | 2 |
| #31826678 | 2 |
| #31826673 | 2 |
| #31826595 | 2 |
| #31826566 | 2 |
| C4×Dic1132 | 2 |
| #495×C283 | 2 |
| #3402 | 283 |