Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 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×#11745270 | C2 | semidirect |
| 2. #14271809 | C2 | semidirect |
| 3. #14271547 | C2 | semidirect |
| 4. #14271409 | C2 | semidirect |
| 5. #14271379 | C2 | semidirect |
| 6. #14271327 | C2 | semidirect |
| 7. #14271299 | C2 | semidirect |
| 8. C4×D232 | C2 | semidirect |
| 9. C29×#436 | C2 | semidirect |
| 11. C22×D116 | C22 | semidirect |
| 12. C2×M16×C29 | C22 | semidirect |
| 16. #11745286 | C22 | semidirect |
| 18. C2×Dic116 | C22 | semidirect |
| 22. C2×#90773 | C22 | semidirect |
| 23. C2×#90773 | C22 | semidirect |
| 27. #11745237 | C22 | semidirect |
| 28. C4×D116 | C22 | semidirect |
| 29. C29×C4⋊C8 | C22 | semidirect |
| 30. C29×C22⋊C8 | C22 | semidirect |
| 31. C4×C8×C29 | C22 | semidirect |
| 32. #11745169 | C22 | semidirect |
| 33. #11745169 | C22 | semidirect |
| 34. #11745166 | C22 | semidirect |
| 35. #11745164 | C22 | semidirect |
| 68. D232 | D4 | semidirect |
| 127. #436 | D29 | semidirect |
| 143. C2×M16 | C2×D29 | semidirect |
| 154. C4⋊C8 | C2×D29 | semidirect |
| 158. C22⋊C8 | C2×D29 | semidirect |
| 159. C4×C8 | C2×D29 | semidirect |
| 160. C29 | #3273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| #14271809 | 2 |
| #14271547 | 2 |
| #14271409 | 2 |
| #14271379 | 2 |
| #14271327 | 2 |
| #14271299 | 2 |
| C4×D232 | 2 |
| C29×#436 | 2 |
| #3273 | 29 |