Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271515 | C2 | semidirect |
| 4. #14271467 | C2 | semidirect |
| 7. #14271373 | C2 | semidirect |
| 8. Q8×#6597 | C2 | semidirect |
| 9. C4×#90785 | C2 | semidirect |
| 11. C29×#557 | C2 | semidirect |
| 112. #557 | D29 | semidirect |
| 156. C29 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271886 | 2 |
| #14271520 | 2 |
| #14271515 | 2 |
| #14271467 | 2 |
| #14271440 | 2 |
| #14271385 | 2 |
| #14271373 | 2 |
| Q8×#6597 | 2 |
| C4×#90785 | 2 |
| C4×#90784 | 2 |
| C29×#557 | 2 |
| #3364 | 29 |