Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
888 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 365 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. #14271033 | C2 | semidirect |
| 4. #14271032 | C2 | semidirect |
| 5. C29×#384 | C2 | semidirect |
| 14. C42×D29 | C4 | semidirect |
| 25. C42×C29 | C2×C4 | semidirect |
| 28. C4×Dic29 | C2×C4 | semidirect |
| 42. C4×D29 | C4⋊C4 | semidirect |
| 51. C4×C29 | C2×C4⋊C4 | semidirect |
| 53. Dic29 | C2×C4⋊C4 | semidirect |
| 58. #384 | D29 | direct (N × H) |
| 62. D29 | #384 | direct (N × H) |
| 72. C29 | C2×#384 | semidirect |
| 86. C42 | C4×D29 | semidirect |
| 110. C4 | C4⋊C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D29 | 2 |
| C2×C42×D29 | 2 |
| #14271033 | 2 |
| #14271032 | 2 |
| C29×#384 | 2 |
| C2×#384 | 29 |