Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#11745158 | C2 | semidirect |
| 5. C2×#11745172 | C2 | semidirect |
| 6. #14270927 | C2 | semidirect |
| 7. C29×#343 | C2 | semidirect |
| 16. #11745271 | C4 | semidirect |
| 116. #343 | D29 | semidirect |
| 144. C29 | #1908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745269 | 2 |
| #14271162 | 2 |
| C2×#11745158 | 2 |
| C2×#11745172 | 2 |
| #14270927 | 2 |
| C29×#343 | 2 |
| #1908 | 29 |