Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 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. #14271878 | C2 | semidirect |
| 2. #14271834 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271488 | C2 | semidirect |
| 5. #14271459 | C2 | semidirect |
| 6. #14271399 | C2 | semidirect |
| 7. #14271359 | C2 | semidirect |
| 8. #14271310 | C2 | semidirect |
| 9. C4×#90773 | C2 | semidirect |
| 10. #14271160 | C2 | semidirect |
| 11. C8×D4×C29 | C2 | semidirect |
| 136. C8×D4 | D29 | semidirect |
| 173. C29 | #3305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271878 | 2 |
| #14271834 | 2 |
| #14271510 | 2 |
| #14271488 | 2 |
| #14271459 | 2 |
| #14271399 | 2 |
| #14271359 | 2 |
| #14271310 | 2 |
| C4×#90773 | 2 |
| #14271160 | 2 |
| C8×D4×C29 | 2 |
| #3305 | 29 |