Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271835 | C2 | semidirect |
| 2. #14271529 | C2 | semidirect |
| 3. #14271511 | C2 | semidirect |
| 4. #14271460 | C2 | semidirect |
| 5. #14271450 | C2 | semidirect |
| 6. #14271358 | C2 | semidirect |
| 7. #14271358 | C2 | semidirect |
| 8. #14271294 | C2 | semidirect |
| 9. #14271273 | C2 | semidirect |
| 10. C4×#90782 | C2 | semidirect |
| 11. C29×#554 | C2 | semidirect |
| 80. D4×C29 | #41 | semidirect |
| 124. #554 | D29 | semidirect |
| 170. C29 | #3366 | semidirect |
| 218. D4 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271835 | 2 |
| #14271529 | 2 |
| #14271511 | 2 |
| #14271460 | 2 |
| #14271450 | 2 |
| #14271358 | 2 |
| #14271294 | 2 |
| #14271273 | 2 |
| C4×#90782 | 2 |
| C29×#554 | 2 |
| #3366 | 29 |