Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31827172 | C2 | semidirect |
| 2. #31827135 | C2 | semidirect |
| 3. #31826828 | C2 | semidirect |
| 4. #31826811 | C2 | semidirect |
| 5. #31826767 | C2 | semidirect |
| 6. #31826756 | C2 | semidirect |
| 7. #31826658 | C2 | semidirect |
| 8. #31826592 | C2 | semidirect |
| 9. #31826577 | C2 | semidirect |
| 10. C4×#17985377 | C2 | semidirect |
| 11. #459×C283 | C2 | semidirect |
| 97. D4×C283 | #41 | semidirect |
| 129. C283 | #3366 | semidirect |
| 138. #459 | D283 | semidirect |
| 218. D4 | #17985391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827172 | 2 |
| #31827135 | 2 |
| #31826828 | 2 |
| #31826811 | 2 |
| #31826767 | 2 |
| #31826756 | 2 |
| #31826658 | 2 |
| #31826592 | 2 |
| #31826577 | 2 |
| C4×#17985377 | 2 |
| #459×C283 | 2 |
| #3366 | 283 |