Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #14271561 | C2 | semidirect |
| 4. #14271502 | C2 | semidirect |
| 5. #14271492 | C2 | semidirect |
| 6. #14271458 | C2 | semidirect |
| 7. #14271448 | C2 | semidirect |
| 8. #14271418 | C2 | semidirect |
| 10. #14271204 | C2 | semidirect |
| 11. C4×Q16×C29 | C2 | semidirect |
| 121. C4×Q16 | D29 | semidirect |
| 157. C29 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271886 | 2 |
| #14271873 | 2 |
| #14271561 | 2 |
| #14271502 | 2 |
| #14271492 | 2 |
| #14271458 | 2 |
| #14271448 | 2 |
| #14271418 | 2 |
| #14271242 | 2 |
| #14271204 | 2 |
| C4×Q16×C29 | 2 |
| #3356 | 29 |