Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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. #14272168 | C2 | semidirect |
| 3. C4×C4⋊#1181 | C2 | semidirect |
| 4. #14272033 | C2 | semidirect |
| 10. C4×D4×C29 | C4 | semidirect |
| 11. D4×Dic29 | C4 | semidirect |
| 15. #11745249 | C4 | semidirect |
| 19. C4×Dic58 | C4 | semidirect |
| 64. D4×C29 | C4⋊C4 | semidirect |
| 87. Dic58 | C4⋊C4 | semidirect |
| 107. Dic29 | #104 | semidirect |
| 128. C4×D4 | #1181 | semidirect |
| 139. C29 | #1806 | semidirect |
| 181. D4 | C4⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272168 | 2 |
| C2×#11745224 | 2 |
| C4×C4⋊#1181 | 2 |
| #14272033 | 2 |
| C4×#90807 | 2 |
| #1806 | 29 |