Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
516 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 189 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. #14271045 | C2 | semidirect |
| 4. #14271014 | C2 | semidirect |
| 6. C42×Dic29 | C2 | semidirect |
| 7. C29×#383 | C2 | semidirect |
| 17. #11745238 | C4 | semidirect |
| 30. C42×C29 | C2×C4 | semidirect |
| 34. #90779 | C2×C4 | semidirect |
| 69. Dic29 | #126 | semidirect |
| 73. #383 | D29 | semidirect |
| 95. C29 | C4×#126 | semidirect |
| 111. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745238 | 2 |
| #14271052 | 2 |
| #14271045 | 2 |
| #14271014 | 2 |
| #14271010 | 2 |
| C42×Dic29 | 2 |
| C29×#383 | 2 |
| C4×#126 | 29 |