Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
264 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 73 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. #14271147 | C2 | semidirect |
| 2. #14271137 | C2 | semidirect |
| 3. #14270953 | C2 | semidirect |
| 4. #14270950 | C2 | semidirect |
| 7. C23×C4×C29 | C4 | semidirect |
| 8. C29×#123 | C4 | semidirect |
| 12. C29×#120 | C4 | semidirect |
| 16. C29×#117 | C4 | semidirect |
| 121. C23×C4 | Dic29 | semidirect |
| 123. #123 | Dic29 | semidirect |
| 127. #120 | Dic29 | semidirect |
| 132. #117 | Dic29 | semidirect |
| 137. C29 | #2120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271147 | 2 |
| #14271137 | 2 |
| #14270953 | 2 |
| #14270950 | 2 |
| C29×#525 | 2 |
| #2120 | 29 |