Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. C2×#11745249 | C2 | semidirect |
| 3. #14271498 | C2 | semidirect |
| 4. #14271473 | C2 | semidirect |
| 5. #14271384 | C2 | semidirect |
| 6. #14271321 | C2 | semidirect |
| 8. #14271269 | C2 | semidirect |
| 9. #14271260 | C2 | semidirect |
| 10. #14271217 | C2 | semidirect |
| 174. C29 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271694 | 2 |
| C2×#11745249 | 2 |
| #14271498 | 2 |
| #14271473 | 2 |
| #14271384 | 2 |
| #14271321 | 2 |
| #14271301 | 2 |
| #14271269 | 2 |
| #14271260 | 2 |
| #14271217 | 2 |
| C29×#481 | 2 |
| #3117 | 29 |