Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14270916 | C2 | semidirect |
| 4. #14270909 | C2 | semidirect |
| 5. C29×#500 | C2 | semidirect |
| 44. C8×C29 | SD16 | semidirect |
| 59. #500 | D29 | semidirect |
| 79. C29 | #1673 | semidirect |
| 109. C8 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271365 | 2 |
| C8×D116 | 2 |
| #14270916 | 2 |
| #14270909 | 2 |
| C29×#500 | 2 |
| #1673 | 29 |