Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11745312 | C2 | semidirect |
| 2. C2×#11745269 | C2 | semidirect |
| 3. #14271744 | C2 | semidirect |
| 4. #14271741 | C2 | semidirect |
| 5. #14271412 | C2 | semidirect |
| 6. #14271408 | C2 | semidirect |
| 7. #14271403 | C2 | semidirect |
| 8. #14271398 | C2 | semidirect |
| 9. C2×#11745155 | C2 | semidirect |
| 10. #14271165 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 82. C2×#6597 | D4 | semidirect |
| 156. #417 | D29 | semidirect |
| 195. C29 | #3061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745312 | 2 |
| C2×#11745269 | 2 |
| #14271744 | 2 |
| #14271741 | 2 |
| #14271412 | 2 |
| #14271408 | 2 |
| #14271403 | 2 |
| #14271398 | 2 |
| C2×#11745155 | 2 |
| #14271165 | 2 |
| C29×#417 | 2 |
| #3061 | 29 |