Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11745311 | C2 | semidirect |
| 2. C22×D232 | C2 | semidirect |
| 3. #14271727 | C2 | semidirect |
| 4. #14271637 | C2 | semidirect |
| 5. #14271381 | C2 | semidirect |
| 6. #14271357 | C2 | semidirect |
| 7. #14271189 | C2 | semidirect |
| 8. #14271167 | C2 | semidirect |
| 9. C29×#416 | C2 | semidirect |
| 16. #11745309 | C22 | semidirect |
| 17. C2×#90784 | C22 | semidirect |
| 18. #11745302 | C22 | semidirect |
| 20. C2×#90782 | C22 | semidirect |
| 26. #11745255 | C22 | semidirect |
| 29. C29×#103 | C22 | semidirect |
| 30. C29×#102 | C22 | semidirect |
| 31. #11745162 | C22 | semidirect |
| 32. #11745157 | C22 | semidirect |
| 48. C2×D116 | D4 | semidirect |
| 124. #416 | D29 | semidirect |
| 151. #103 | C2×D29 | semidirect |
| 153. #102 | C2×D29 | semidirect |
| 154. C29 | #3041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C22×D232 | 2 |
| #14271727 | 2 |
| #14271637 | 2 |
| #14271381 | 2 |
| #14271357 | 2 |
| #14271189 | 2 |
| #14271167 | 2 |
| C29×#416 | 2 |
| #3041 | 29 |