Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
168 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 87 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. #14270941 | C2 | semidirect |
| 4. #14270940 | C2 | semidirect |
| 5. C29×#347 | C2 | semidirect |
| 15. #11745146 | C4 | semidirect |
| 16. C16×D29 | C4 | semidirect |
| 30. C16×C29 | C2×C4 | semidirect |
| 31. #90768 | C2×C4 | semidirect |
| 61. #347 | D29 | direct (N × H) |
| 65. D29 | #347 | direct (N × H) |
| 77. C29 | C2×#347 | semidirect |
| 92. C16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D29 | 2 |
| #97×D29 | 2 |
| #14270941 | 2 |
| #14270940 | 2 |
| C29×#347 | 2 |
| C2×#347 | 29 |