Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 565 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. #14271789 | C2 | direct (N × H) |
| 2. C2×#11745286 | C2 | semidirect |
| 3. C2×#11745240 | C2 | semidirect |
| 9. C22×Dic58 | C22 | semidirect |
| 15. C2×C4⋊Dic29 | C22 | semidirect |
| 16. #11745286 | C22 | semidirect |
| 17. C2×#90779 | C22 | semidirect |
| 18. #11745240 | C22 | semidirect |
| 20. C24×C29 | Q8 | semidirect |
| 31. C2×Dic58 | C23 | semidirect |
| 35. C4⋊Dic29 | C23 | semidirect |
| 36. #90779 | C23 | semidirect |
| 43. C23×C29 | C2×Q8 | semidirect |
| 74. C2×C29 | #543 | semidirect |
| 90. C29 | C2×#543 | semidirect |
| 92. C24 | Dic58 | semidirect |
| 115. C23 | C2×Dic58 | semidirect |
| 140. C2 | #14271789 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271789 | 2 |
| C2×#11745286 | 2 |
| C2×#11745240 | 2 |
| C22×C22⋊Dic29 | 2 |
| C22×C22⋊C4×C29 | 2 |
| C2×#543 | 29 |