Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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×#11745155 | C2 | semidirect |
| 5. #14270926 | C2 | semidirect |
| 6. #14270925 | C2 | semidirect |
| 7. C2×C29×#107 | C2 | semidirect |
| 22. #11745168 | C4 | semidirect |
| 42. C2×C8×C29 | C2×C4 | semidirect |
| 55. C2×#6597 | C2×C4 | semidirect |
| 106. C2×D29 | #107 | semidirect |
| 118. C2×#107 | D29 | semidirect |
| 147. C29 | #1852 | semidirect |
| 169. C2×C8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D29 | 2 |
| C2×#11745155 | 2 |
| C2×#11745168 | 2 |
| #14271020 | 2 |
| #14270926 | 2 |
| #14270925 | 2 |
| C2×C29×#107 | 2 |
| #1852 | 29 |