Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 2. #14271529 | C2 | semidirect |
| 3. #14271525 | C2 | semidirect |
| 4. #14271520 | C2 | semidirect |
| 5. #14271511 | C2 | semidirect |
| 6. #14271167 | C2 | semidirect |
| 7. #14271162 | C2 | semidirect |
| 8. #14271157 | C2 | semidirect |
| 9. C2×#11745157 | C2 | semidirect |
| 10. #14271119 | C2 | semidirect |
| 11. C29×#544 | C2 | semidirect |
| 15. C29×C4⋊Q8 | C22 | semidirect |
| 17. C29×#125 | C22 | semidirect |
| 29. #11745158 | C22 | semidirect |
| 30. #11745158 | C22 | semidirect |
| 31. #11745158 | C22 | semidirect |
| 36. #11745157 | C22 | semidirect |
| 37. #11745157 | C22 | semidirect |
| 38. #11745157 | C22 | semidirect |
| 39. #11745151 | C22 | semidirect |
| 40. C4×#6597 | C22 | semidirect |
| 130. #544 | D29 | semidirect |
| 152. C4⋊Q8 | C2×D29 | semidirect |
| 155. #125 | C2×D29 | semidirect |
| 176. C29 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271732 | 2 |
| #14271529 | 2 |
| #14271525 | 2 |
| #14271520 | 2 |
| #14271511 | 2 |
| #14271167 | 2 |
| #14271162 | 2 |
| #14271157 | 2 |
| C2×#11745157 | 2 |
| #14271119 | 2 |
| C29×#544 | 2 |
| #3136 | 29 |