Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14271859 | C2 | semidirect |
| 2. #14271565 | C2 | semidirect |
| 3. #14271488 | C2 | semidirect |
| 4. #14271477 | C2 | semidirect |
| 5. #14271464 | C2 | semidirect |
| 6. #14271416 | C2 | semidirect |
| 7. C4×D232 | C2 | semidirect |
| 8. #14271205 | C2 | semidirect |
| 9. C29×#436 | C2 | semidirect |
| 105. #436 | D29 | semidirect |
| 137. C29 | #3355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271859 | 2 |
| #14271565 | 2 |
| #14271488 | 2 |
| #14271477 | 2 |
| #14271464 | 2 |
| #14271416 | 2 |
| C4×D232 | 2 |
| #14271205 | 2 |
| C29×#436 | 2 |
| #3355 | 29 |