Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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. C4×#90796 | C2 | semidirect |
| 3. #14272099 | C2 | semidirect |
| 4. #14272033 | C2 | semidirect |
| 9. C4×Q8×C29 | C4 | semidirect |
| 10. Q8×Dic29 | C4 | semidirect |
| 12. #11745255 | C4 | semidirect |
| 16. C4×D116 | C4 | semidirect |
| 19. #11745226 | C4 | semidirect |
| 38. C4×#1181 | C2×C4 | semidirect |
| 40. #90796 | C2×C4 | semidirect |
| 114. C4×Q8 | #1181 | semidirect |
| 129. C29 | #1759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745226 | 2 |
| C4×#90796 | 2 |
| #14272099 | 2 |
| #14272033 | 2 |
| C4×#90809 | 2 |
| #1759 | 29 |