Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #14271778 | C2 | semidirect |
| 2. #14271560 | C2 | semidirect |
| 3. #14271546 | C2 | semidirect |
| 4. #14271521 | C2 | semidirect |
| 5. #14271422 | C2 | semidirect |
| 7. #14271391 | C2 | semidirect |
| 8. #14271271 | C2 | semidirect |
| 9. C4×#90783 | C2 | semidirect |
| 10. #14271120 | C2 | semidirect |
| 11. C29×#442 | C2 | semidirect |
| 113. #442 | D29 | semidirect |
| 148. C29 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271778 | 2 |
| #14271560 | 2 |
| #14271546 | 2 |
| #14271521 | 2 |
| #14271422 | 2 |
| #14271413 | 2 |
| #14271391 | 2 |
| #14271271 | 2 |
| C4×#90783 | 2 |
| #14271120 | 2 |
| C29×#442 | 2 |
| #3173 | 29 |