Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #14271886 | C2 | semidirect |
| 3. #14271513 | C2 | semidirect |
| 4. #14271503 | C2 | semidirect |
| 5. #14271444 | C2 | semidirect |
| 6. #14271401 | C2 | semidirect |
| 7. #14271324 | C2 | semidirect |
| 8. C4×#90784 | C2 | semidirect |
| 9. #14271228 | C2 | semidirect |
| 10. #14271158 | C2 | semidirect |
| 11. C29×#462 | C2 | semidirect |
| 127. #462 | D29 | semidirect |
| 166. C29 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271886 | 2 |
| #14271816 | 2 |
| #14271513 | 2 |
| #14271503 | 2 |
| #14271444 | 2 |
| #14271401 | 2 |
| #14271324 | 2 |
| C4×#90784 | 2 |
| #14271228 | 2 |
| #14271158 | 2 |
| C29×#462 | 2 |
| #3302 | 29 |