Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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. #14271874 | C2 | semidirect |
| 2. #14271834 | C2 | semidirect |
| 3. #14271526 | C2 | semidirect |
| 4. #14271511 | C2 | semidirect |
| 5. #14271462 | C2 | semidirect |
| 6. #14271359 | C2 | semidirect |
| 7. #14271357 | C2 | semidirect |
| 8. #14271290 | C2 | semidirect |
| 9. #14271274 | C2 | semidirect |
| 10. C4×#90782 | C2 | semidirect |
| 11. C29×#476 | C2 | semidirect |
| 96. D116 | #41 | semidirect |
| 129. #476 | D29 | semidirect |
| 170. C29 | #3366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271874 | 2 |
| #14271834 | 2 |
| #14271526 | 2 |
| #14271511 | 2 |
| #14271462 | 2 |
| #14271359 | 2 |
| #14271357 | 2 |
| #14271290 | 2 |
| #14271274 | 2 |
| C4×#90782 | 2 |
| C29×#476 | 2 |
| #3366 | 29 |