Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C2×#11745167 | C2 | semidirect |
| 3. #14271189 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C29×#336 | C2 | semidirect |
| 19. #11745169 | C4 | semidirect |
| 20. #11745169 | C4 | semidirect |
| 22. #11745164 | C4 | semidirect |
| 23. #11745164 | C4 | semidirect |
| 110. #336 | D29 | semidirect |
| 136. C29 | #1866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745263 | 2 |
| C2×#11745167 | 2 |
| #14271189 | 2 |
| C2×#11745153 | 2 |
| #14271160 | 2 |
| #14270923 | 2 |
| C29×#336 | 2 |
| #1866 | 29 |