Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #14271870 | C2 | semidirect |
| 3. #14271568 | C2 | semidirect |
| 4. #14271505 | C2 | semidirect |
| 5. #14271477 | C2 | semidirect |
| 6. #14271459 | C2 | semidirect |
| 7. #14271454 | C2 | semidirect |
| 8. #14271409 | C2 | semidirect |
| 9. C4×#90773 | C2 | semidirect |
| 10. #14271205 | C2 | semidirect |
| 11. C29×#436 | C2 | semidirect |
| 126. #436 | D29 | semidirect |
| 162. C29 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271878 | 2 |
| #14271870 | 2 |
| #14271568 | 2 |
| #14271505 | 2 |
| #14271477 | 2 |
| #14271459 | 2 |
| #14271454 | 2 |
| #14271409 | 2 |
| C4×#90773 | 2 |
| #14271205 | 2 |
| C29×#436 | 2 |
| #3357 | 29 |