Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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. #14272134 | C2 | semidirect |
| 2. C2×(C2×#1181)⋊C4 | C2 | semidirect |
| 3. #14272016 | C2 | semidirect |
| 4. #14272014 | C2 | semidirect |
| 7. C2×#90807 | C4 | semidirect |
| 10. C29×#121 | C4 | semidirect |
| 14. #11745286 | C4 | semidirect |
| 16. #11745254 | C4 | semidirect |
| 29. C2×D4×C29 | C2×C4 | semidirect |
| 41. C2×Dic58 | C2×C4 | semidirect |
| 44. C4⋊C4×C29 | C2×C4 | semidirect |
| 51. C4⋊Dic29 | C2×C4 | semidirect |
| 133. #121 | #1181 | semidirect |
| 142. C29 | #1504 | semidirect |
| 149. C2×D4 | C2×#1181 | semidirect |
| 167. C4⋊C4 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272134 | 2 |
| C2×(C2×#1181)⋊C4 | 2 |
| #14272016 | 2 |
| #14272014 | 2 |
| #14271673 | 2 |
| #1504 | 29 |