Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
310 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 66 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. #14272231 | C2 | semidirect |
| 3. #14272156 | C2 | semidirect |
| 5. #14272045 | C2 | semidirect |
| 6. #14272031 | C2 | semidirect |
| 17. C2×SD16×C29 | C4 | semidirect |
| 18. C2×#90785 | C4 | semidirect |
| 19. C2×#90783 | C4 | semidirect |
| 22. C2×Dic116 | C4 | semidirect |
| 135. C2×SD16 | #1181 | semidirect |
| 147. C29 | #1905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272231 | 2 |
| #14272161 | 2 |
| #14272156 | 2 |
| #14272143 | 2 |
| #14272045 | 2 |
| #14272031 | 2 |
| C2×#11745277 | 2 |
| #1905 | 29 |