Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #14271507 | C2 | semidirect |
| 4. #14271506 | C2 | semidirect |
| 5. #14271500 | C2 | semidirect |
| 6. #14271495 | C2 | semidirect |
| 7. #14271206 | C2 | semidirect |
| 8. #14271171 | C2 | semidirect |
| 9. C2×#11745164 | C2 | semidirect |
| 11. C29×#427 | C2 | semidirect |
| 129. #427 | D29 | semidirect |
| 167. C29 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271739 | 2 |
| #14271643 | 2 |
| #14271507 | 2 |
| #14271506 | 2 |
| #14271500 | 2 |
| #14271495 | 2 |
| #14271206 | 2 |
| #14271171 | 2 |
| C2×#11745164 | 2 |
| #14271129 | 2 |
| C29×#427 | 2 |
| #3097 | 29 |