Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745304 | C2 | semidirect |
| 2. C2×#11745313 | C2 | semidirect |
| 4. C22×#90785 | C2 | semidirect |
| 5. #14271739 | C2 | semidirect |
| 6. #14271558 | C2 | semidirect |
| 7. #14271555 | C2 | semidirect |
| 8. #14271545 | C2 | semidirect |
| 9. #14271542 | C2 | semidirect |
| 10. #14271119 | C2 | semidirect |
| 11. C29×#536 | C2 | semidirect |
| 144. #536 | D29 | semidirect |
| 186. C29 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| C2×#11745313 | 2 |
| C2×#11745312 | 2 |
| C22×#90785 | 2 |
| #14271739 | 2 |
| #14271558 | 2 |
| #14271555 | 2 |
| #14271545 | 2 |
| #14271542 | 2 |
| #14271119 | 2 |
| C29×#536 | 2 |
| #3156 | 29 |