Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#11745294 | C2 | semidirect |
| 3. C2×#11745302 | C2 | semidirect |
| 4. #14271631 | C2 | semidirect |
| 5. #14271362 | C2 | semidirect |
| 6. #14271357 | C2 | semidirect |
| 7. #14271186 | C2 | semidirect |
| 8. #14271167 | C2 | semidirect |
| 9. C29×#418 | C2 | semidirect |
| 19. C2×#90783 | C22 | semidirect |
| 21. C2×#90782 | C22 | semidirect |
| 25. C2×D232 | C22 | semidirect |
| 26. C2×#90773 | C22 | semidirect |
| 27. #11745255 | C22 | semidirect |
| 28. #11745249 | C22 | semidirect |
| 32. C29×#102 | C22 | semidirect |
| 33. #11745162 | C22 | semidirect |
| 34. #11745157 | C22 | semidirect |
| 48. #90805 | D4 | semidirect |
| 101. D116 | C2×D4 | semidirect |
| 105. Dic58 | C2×D4 | semidirect |
| 126. Dic29 | AGL(1,ℤ/8) | semidirect |
| 135. #418 | D29 | semidirect |
| 166. #102 | C2×D29 | semidirect |
| 167. C29 | #3038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| C2×#11745294 | 2 |
| C2×#11745302 | 2 |
| #14271631 | 2 |
| #14271362 | 2 |
| #14271357 | 2 |
| #14271186 | 2 |
| #14271167 | 2 |
| C29×#418 | 2 |
| #3038 | 29 |