Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
488 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 146 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 |
|---|---|---|
| 3. #14272033 | C2 | direct (N × H) |
| 10. C2×C4×#1181 | C4 | semidirect |
| 14. C2×#90796 | C4 | semidirect |
| 16. C2×C4⋊C4×C29 | C4 | semidirect |
| 18. C2×C4⋊Dic29 | C4 | semidirect |
| 22. #11745254 | C4 | semidirect |
| 45. C4×#1181 | C2×C4 | semidirect |
| 48. #90796 | C2×C4 | semidirect |
| 50. C4⋊C4×C29 | C2×C4 | semidirect |
| 54. C4⋊Dic29 | C2×C4 | semidirect |
| 118. C2×C29 | #339 | semidirect |
| 137. C2×C4⋊C4 | #1181 | semidirect |
| 144. C29 | C2×#339 | semidirect |
| 170. C4⋊C4 | C2×#1181 | semidirect |
| 237. C2 | #14272033 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90796 | 2 |
| C22×C4×#1181 | 2 |
| #14272033 | 2 |
| C2×#11745254 | 2 |
| C2×#339 | 29 |