Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 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. #14271718 | C2 | semidirect |
| 3. #14271507 | C2 | semidirect |
| 4. #14271455 | C2 | semidirect |
| 5. #14271374 | C2 | semidirect |
| 6. #14271368 | C2 | semidirect |
| 8. #14271269 | C2 | semidirect |
| 9. #14271260 | C2 | semidirect |
| 10. #14271219 | C2 | semidirect |
| 11. C29×#476 | C2 | semidirect |
| 136. #476 | D29 | semidirect |
| 179. C29 | #3116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| C4×#90807 | 2 |
| #14271507 | 2 |
| #14271455 | 2 |
| #14271374 | 2 |
| #14271368 | 2 |
| #14271326 | 2 |
| #14271269 | 2 |
| #14271260 | 2 |
| #14271219 | 2 |
| C29×#476 | 2 |
| #3116 | 29 |