Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. #14271714 | C2 | semidirect |
| 2. #14271698 | C2 | semidirect |
| 3. #14271552 | C2 | semidirect |
| 4. #14271529 | C2 | semidirect |
| 5. #14271525 | C2 | semidirect |
| 6. #14271417 | C2 | semidirect |
| 7. #14271410 | C2 | semidirect |
| 8. #14271250 | C2 | semidirect |
| 9. #14271245 | C2 | semidirect |
| 10. #14271115 | C2 | semidirect |
| 11. C29×#501 | C2 | semidirect |
| 109. C8×C29 | #41 | semidirect |
| 134. #501 | D29 | semidirect |
| 180. C29 | #3171 | semidirect |
| 248. C8 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271714 | 2 |
| #14271698 | 2 |
| #14271552 | 2 |
| #14271529 | 2 |
| #14271525 | 2 |
| #14271417 | 2 |
| #14271410 | 2 |
| #14271250 | 2 |
| #14271245 | 2 |
| #14271115 | 2 |
| C29×#501 | 2 |
| #3171 | 29 |