Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14271187 | C2 | semidirect |
| 4. #14270923 | C2 | semidirect |
| 5. C4×C4⋊C4×C29 | C2 | semidirect |
| 14. C4×D116 | C4 | semidirect |
| 15. C4×D116 | C4 | semidirect |
| 18. C4×Dic58 | C4 | semidirect |
| 19. C4×Dic58 | C4 | semidirect |
| 81. D116 | C4⋊C4 | semidirect |
| 87. Dic58 | C4⋊C4 | semidirect |
| 102. C4×C29 | #104 | semidirect |
| 113. C4×C4⋊C4 | D29 | semidirect |
| 139. C29 | #1806 | semidirect |
| 220. C4 | #11745153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90805 | 2 |
| #14271187 | 2 |
| C2×#11745153 | 2 |
| #14270923 | 2 |
| C4×C4⋊C4×C29 | 2 |
| #1806 | 29 |