Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271699 | C2 | semidirect |
| 2. C2×#11745255 | C2 | semidirect |
| 3. #14271476 | C2 | semidirect |
| 4. #14271462 | C2 | semidirect |
| 5. #14271381 | C2 | semidirect |
| 6. #14271313 | C2 | semidirect |
| 8. #14271274 | C2 | semidirect |
| 9. #14271266 | C2 | semidirect |
| 10. #14271217 | C2 | semidirect |
| 11. C29×#483 | C2 | semidirect |
| 16. #11745309 | C22 | semidirect |
| 17. Q8×Dic29 | C22 | semidirect |
| 28. #11745255 | C22 | semidirect |
| 30. #11745252 | C22 | semidirect |
| 33. C29×#106 | C22 | semidirect |
| 34. C29×#103 | C22 | semidirect |
| 38. #11745163 | C22 | semidirect |
| 39. #11745162 | C22 | semidirect |
| 41. #11745157 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 137. #483 | D29 | semidirect |
| 174. #106 | C2×D29 | semidirect |
| 176. #103 | C2×D29 | semidirect |
| 183. C29 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271699 | 2 |
| C2×#11745255 | 2 |
| #14271476 | 2 |
| #14271462 | 2 |
| #14271381 | 2 |
| #14271313 | 2 |
| #14271299 | 2 |
| #14271274 | 2 |
| #14271266 | 2 |
| #14271217 | 2 |
| C29×#483 | 2 |
| #3114 | 29 |