Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#11745266 | C2 | semidirect |
| 2. #14271604 | C2 | semidirect |
| 3. #14271603 | C2 | semidirect |
| 4. #14271599 | C2 | semidirect |
| 5. #14271598 | C2 | semidirect |
| 6. #14271593 | C2 | semidirect |
| 7. C2×#11745160 | C2 | semidirect |
| 8. C2×C29×#135 | C2 | semidirect |
| 14. C29×#135 | C22 | semidirect |
| 15. C2×Q16×C29 | C22 | semidirect |
| 17. C2×D8×C29 | C22 | semidirect |
| 19. C2×Dic116 | C22 | semidirect |
| 23. #11745266 | C22 | semidirect |
| 24. C2×D232 | C22 | semidirect |
| 26. #11745177 | C22 | semidirect |
| 27. #11745176 | C22 | semidirect |
| 28. #11745175 | C22 | semidirect |
| 29. #11745174 | C22 | semidirect |
| 30. #11745160 | C22 | semidirect |
| 31. #11745160 | C22 | semidirect |
| 32. C2×#90768 | C22 | semidirect |
| 116. C2×#135 | D29 | semidirect |
| 138. #135 | C2×D29 | semidirect |
| 140. C2×Q16 | C2×D29 | semidirect |
| 144. C2×D8 | C2×D29 | semidirect |
| 153. C29 | #3414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| #14271604 | 2 |
| #14271603 | 2 |
| #14271599 | 2 |
| #14271598 | 2 |
| #14271593 | 2 |
| C2×#11745160 | 2 |
| C2×C29×#135 | 2 |
| #3414 | 29 |