Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14271870 | C2 | semidirect |
| 2. #14271566 | C2 | semidirect |
| 3. #14271504 | C2 | semidirect |
| 4. #14271474 | C2 | semidirect |
| 5. #14271455 | C2 | semidirect |
| 6. #14271453 | C2 | semidirect |
| 7. #14271407 | C2 | semidirect |
| 8. C4×#90783 | C2 | semidirect |
| 9. #14271241 | C2 | semidirect |
| 10. #14271206 | C2 | semidirect |
| 162. C29 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271870 | 2 |
| #14271566 | 2 |
| #14271504 | 2 |
| #14271474 | 2 |
| #14271455 | 2 |
| #14271453 | 2 |
| #14271407 | 2 |
| C4×#90783 | 2 |
| #14271241 | 2 |
| #14271206 | 2 |
| C29×#555 | 2 |
| #3357 | 29 |