Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14271713 | C2 | semidirect |
| 2. #14271697 | C2 | semidirect |
| 3. #14271572 | C2 | semidirect |
| 4. #14271552 | C2 | semidirect |
| 5. #14271528 | C2 | semidirect |
| 6. #14271523 | C2 | semidirect |
| 7. #14271416 | C2 | semidirect |
| 8. #14271409 | C2 | semidirect |
| 9. C4×#90773 | C2 | semidirect |
| 10. C4×D232 | C2 | semidirect |
| 11. C4×M16×C29 | C2 | semidirect |
| 110. C8×C29 | #41 | semidirect |
| 142. C4×M16 | D29 | semidirect |
| 180. C29 | #3171 | semidirect |
| 248. C8 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271713 | 2 |
| #14271697 | 2 |
| #14271572 | 2 |
| #14271552 | 2 |
| #14271528 | 2 |
| #14271523 | 2 |
| #14271416 | 2 |
| #14271409 | 2 |
| C4×#90773 | 2 |
| C4×D232 | 2 |
| C4×M16×C29 | 2 |
| #3171 | 29 |