Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #14271791 | C2 | semidirect |
| 3. #14271465 | C2 | semidirect |
| 4. #14271461 | C2 | semidirect |
| 5. #14271451 | C2 | semidirect |
| 6. #14271441 | C2 | semidirect |
| 7. #14271205 | C2 | semidirect |
| 8. #14271199 | C2 | semidirect |
| 9. #14271191 | C2 | semidirect |
| 24. #11745252 | C22 | semidirect |
| 25. #11745250 | C22 | semidirect |
| 33. #11745166 | C22 | semidirect |
| 34. #11745165 | C22 | semidirect |
| 35. #11745162 | C22 | semidirect |
| 36. #11745162 | C22 | semidirect |
| 37. #11745156 | C22 | semidirect |
| 38. #11745156 | C22 | semidirect |
| 39. #11745155 | C22 | semidirect |
| 40. #11745155 | C22 | semidirect |
| 44. C2×D4×C29 | Q8 | semidirect |
| 165. C29 | #3081 | semidirect |
| 170. C2×D4 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271791 | 2 |
| #14271638 | 2 |
| #14271465 | 2 |
| #14271461 | 2 |
| #14271451 | 2 |
| #14271441 | 2 |
| #14271205 | 2 |
| #14271199 | 2 |
| #14271191 | 2 |
| C2×#11745180 | 2 |
| C29×#418 | 2 |
| #3081 | 29 |