Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 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. #14271720 | C2 | semidirect |
| 3. #14271572 | C2 | semidirect |
| 4. #14271557 | C2 | semidirect |
| 5. #14271532 | C2 | semidirect |
| 6. #14271523 | C2 | semidirect |
| 7. #14271421 | C2 | semidirect |
| 9. C4×Dic116 | C2 | semidirect |
| 10. C4×#90773 | C2 | semidirect |
| 11. C4×M16×C29 | C2 | semidirect |
| 135. C4×M16 | D29 | semidirect |
| 172. C29 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271697 | 2 |
| #14271572 | 2 |
| #14271557 | 2 |
| #14271532 | 2 |
| #14271523 | 2 |
| #14271421 | 2 |
| #14271409 | 2 |
| C4×Dic116 | 2 |
| C4×#90773 | 2 |
| C4×M16×C29 | 2 |
| #3172 | 29 |