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×#90809 | C2 | semidirect |
| 3. #14271485 | C2 | semidirect |
| 4. #14271448 | C2 | semidirect |
| 5. #14271444 | C2 | semidirect |
| 6. #14271355 | C2 | semidirect |
| 7. #14271307 | C2 | semidirect |
| 8. #14271272 | C2 | semidirect |
| 9. #14271264 | C2 | semidirect |
| 10. #14271219 | C2 | semidirect |
| 11. C29×#460 | C2 | semidirect |
| 87. Q8×C29 | #41 | semidirect |
| 106. D116 | #41 | semidirect |
| 144. #460 | D29 | semidirect |
| 187. C29 | #3115 | semidirect |
| 233. Q8 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271711 | 2 |
| C4×#90809 | 2 |
| #14271485 | 2 |
| #14271448 | 2 |
| #14271444 | 2 |
| #14271355 | 2 |
| #14271307 | 2 |
| #14271272 | 2 |
| #14271264 | 2 |
| #14271219 | 2 |
| C29×#460 | 2 |
| #3115 | 29 |