Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745271 | C2 | semidirect |
| 3. C22×#90785 | C2 | semidirect |
| 4. #14271737 | C2 | semidirect |
| 5. #14271734 | C2 | semidirect |
| 6. #14271556 | C2 | semidirect |
| 7. #14271554 | C2 | semidirect |
| 8. #14271544 | C2 | semidirect |
| 9. #14271541 | C2 | semidirect |
| 10. #14271121 | C2 | semidirect |
| 11. C2×C29×#137 | C2 | semidirect |
| 140. C2×#137 | D29 | semidirect |
| 186. C29 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745312 | 2 |
| C22×#90785 | 2 |
| #14271737 | 2 |
| #14271734 | 2 |
| #14271556 | 2 |
| #14271554 | 2 |
| #14271544 | 2 |
| #14271541 | 2 |
| #14271121 | 2 |
| C2×C29×#137 | 2 |
| #3156 | 29 |