Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #14271119 | C2 | semidirect |
| 5. C2×#11745151 | C2 | semidirect |
| 6. #14270927 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 16. #11745269 | C4 | semidirect |
| 19. #11745158 | C4 | semidirect |
| 20. #11745157 | C4 | semidirect |
| 21. #11745153 | C4 | semidirect |
| 100. #339 | D29 | semidirect |
| 123. C29 | #1765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745269 | 2 |
| C2×#11745153 | 2 |
| #14271157 | 2 |
| #14271119 | 2 |
| C2×#11745151 | 2 |
| #14270927 | 2 |
| C29×#339 | 2 |
| #1765 | 29 |