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 |
|---|---|---|
| 2. #14271460 | C2 | semidirect |
| 3. #14271460 | C2 | semidirect |
| 4. #14271450 | C2 | semidirect |
| 5. #14271440 | C2 | semidirect |
| 6. #14271203 | C2 | semidirect |
| 7. #14271199 | C2 | semidirect |
| 8. #14271190 | C2 | semidirect |
| 11. C29×#544 | C2 | semidirect |
| 14. C29×C4⋊Q8 | C22 | semidirect |
| 16. C29×#125 | C22 | semidirect |
| 33. #11745156 | C22 | semidirect |
| 34. #11745156 | C22 | semidirect |
| 35. #11745156 | C22 | semidirect |
| 36. #11745155 | C22 | semidirect |
| 37. #11745155 | C22 | semidirect |
| 38. #11745155 | C22 | semidirect |
| 39. C4⋊#6597 | C22 | semidirect |
| 40. C4⋊#6597 | C22 | semidirect |
| 47. C2×D116 | Q8 | semidirect |
| 120. #544 | D29 | semidirect |
| 140. C4⋊Q8 | C2×D29 | semidirect |
| 142. #125 | C2×D29 | semidirect |
| 165. C29 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271637 | 2 |
| #14271460 | 2 |
| #14271450 | 2 |
| #14271440 | 2 |
| #14271203 | 2 |
| #14271199 | 2 |
| #14271190 | 2 |
| #14271167 | 2 |
| C2×#11745157 | 2 |
| C29×#544 | 2 |
| #3081 | 29 |