Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #14271930 | C2 | semidirect |
| 3. #14271181 | C2 | semidirect |
| 4. C2×#11745153 | C2 | semidirect |
| 5. C4×#41×C29 | C2 | semidirect |
| 7. #11745365 | C4 | semidirect |
| 8. #11745364 | C4 | semidirect |
| 15. C29×#117 | C22 | semidirect |
| 16. C2×C42×C29 | C22 | semidirect |
| 18. C2×#90777 | C22 | semidirect |
| 19. #11745153 | C22 | semidirect |
| 20. #11745153 | C22 | semidirect |
| 34. #90805 | C2×C4 | semidirect |
| 36. C2×D116 | C2×C4 | semidirect |
| 38. C2×Dic58 | C2×C4 | semidirect |
| 82. C4×#41 | D29 | semidirect |
| 100. #117 | C2×D29 | semidirect |
| 101. C2×C42 | C2×D29 | semidirect |
| 104. C29 | #2901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271999 | 2 |
| #14271930 | 2 |
| #14271181 | 2 |
| C2×#11745153 | 2 |
| C4×#41×C29 | 2 |
| #2901 | 29 |