Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. C2×#11745166 | C2 | semidirect |
| 2. C2×#11745165 | C2 | semidirect |
| 6. #14271029 | C2 | semidirect |
| 7. C29×#336 | C2 | semidirect |
| 100. #336 | D29 | semidirect |
| 120. C29 | #2092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745166 | 2 |
| C2×#11745165 | 2 |
| C2×#11745169 | 2 |
| #14271065 | 2 |
| #14271029 | 2 |
| C29×#336 | 2 |
| #2092 | 29 |