Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#11745237 | C2 | semidirect |
| 4. C4×#90805 | C2 | semidirect |
| 5. #14271386 | C2 | semidirect |
| 6. #14271379 | C2 | semidirect |
| 7. #14271173 | C2 | semidirect |
| 8. #14271169 | C2 | semidirect |
| 9. C29×#423 | C2 | semidirect |
| 21. C2×Dic116 | C22 | semidirect |
| 24. C2×#90773 | C22 | semidirect |
| 28. C4×D116 | C22 | semidirect |
| 31. C4×Dic58 | C22 | semidirect |
| 32. C29×C4⋊C8 | C22 | semidirect |
| 34. #11745164 | C22 | semidirect |
| 127. #423 | D29 | semidirect |
| 157. C4⋊C8 | C2×D29 | semidirect |
| 160. C29 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745270 | 2 |
| C2×#11745237 | 2 |
| C4×#90805 | 2 |
| #14271386 | 2 |
| #14271379 | 2 |
| #14271173 | 2 |
| #14271169 | 2 |
| C29×#423 | 2 |
| #3040 | 29 |