Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 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. #14271711 | C2 | semidirect |
| 2. C4×#90807 | C2 | semidirect |
| 3. #14271486 | C2 | semidirect |
| 4. #14271449 | C2 | semidirect |
| 5. #14271443 | C2 | semidirect |
| 6. #14271360 | C2 | semidirect |
| 7. #14271305 | C2 | semidirect |
| 8. #14271275 | C2 | semidirect |
| 9. #14271260 | C2 | semidirect |
| 10. #14271219 | C2 | semidirect |
| 11. C29×#459 | C2 | semidirect |
| 91. D4×C29 | #41 | semidirect |
| 114. Dic58 | #41 | semidirect |
| 145. #459 | D29 | semidirect |
| 187. C29 | #3115 | semidirect |
| 241. D4 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271711 | 2 |
| C4×#90807 | 2 |
| #14271486 | 2 |
| #14271449 | 2 |
| #14271443 | 2 |
| #14271360 | 2 |
| #14271305 | 2 |
| #14271275 | 2 |
| #14271260 | 2 |
| #14271219 | 2 |
| C29×#459 | 2 |
| #3115 | 29 |