Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
656 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 285 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. #14271061 | C2 | semidirect |
| 5. C4×#90779 | C2 | semidirect |
| 15. #11745288 | C4 | semidirect |
| 38. C4⋊Dic29 | C2×C4 | semidirect |
| 41. C4×Dic29 | C2×C4 | semidirect |
| 50. C2×C4×C29 | C4⋊C4 | semidirect |
| 102. C29 | #2296 | semidirect |
| 135. C2×C4 | #90779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745288 | 2 |
| #14271061 | 2 |
| #14271036 | 2 |
| C4×#90779 | 2 |
| C22×C42×C29 | 2 |
| #2296 | 29 |