Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
688 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 169 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×#11745291 | C2 | semidirect |
| 3. C22×C4×Dic29 | C2 | semidirect |
| 4. #14271063 | C2 | semidirect |
| 5. #14271058 | C2 | semidirect |
| 6. #14271057 | C2 | semidirect |
| 7. #14271053 | C2 | semidirect |
| 8. #14271043 | C2 | semidirect |
| 9. #14271040 | C2 | semidirect |
| 10. #14271021 | C2 | semidirect |
| 11. C2×C29×#123 | C2 | semidirect |
| 47. C22×C4×C29 | D4 | semidirect |
| 151. Dic29 | #123 | semidirect |
| 153. C2×#123 | D29 | semidirect |
| 198. C29 | #2854 | semidirect |
| 221. C22×C4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745291 | 2 |
| C2×#11745301 | 2 |
| C22×C4×Dic29 | 2 |
| #14271063 | 2 |
| #14271058 | 2 |
| #14271057 | 2 |
| #14271053 | 2 |
| #14271043 | 2 |
| #14271040 | 2 |
| #14271021 | 2 |
| C2×C29×#123 | 2 |
| #2854 | 29 |