Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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×#11745212 | C2 | semidirect |
| 2. #14272173 | C2 | semidirect |
| 4. #14272046 | C2 | semidirect |
| 9. C29×#131 | C4 | semidirect |
| 10. #11745310 | C4 | semidirect |
| 12. #11745269 | C4 | semidirect |
| 16. #11745263 | C4 | semidirect |
| 123. #131 | #1181 | semidirect |
| 136. C29 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745212 | 2 |
| #14272173 | 2 |
| #14272160 | 2 |
| #14272046 | 2 |
| #131×D29 | 2 |
| #1814 | 29 |