Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#11745281 | C2 | semidirect |
| 2. C2×M16×D29 | C2 | semidirect |
| 3. #14271676 | C2 | semidirect |
| 4. #14271418 | C2 | semidirect |
| 5. #14271417 | C2 | semidirect |
| 6. #14271416 | C2 | semidirect |
| 7. #14271412 | C2 | semidirect |
| 8. #14271411 | C2 | semidirect |
| 9. #14271198 | C2 | semidirect |
| 10. #14271158 | C2 | semidirect |
| 11. C29×#470 | C2 | semidirect |
| 14. C2×Q16×C29 | C22 | semidirect |
| 18. C2×#90784 | C22 | semidirect |
| 23. C2×D232 | C22 | semidirect |
| 34. C29×#106 | C22 | semidirect |
| 35. C29×#103 | C22 | semidirect |
| 36. #11745183 | C22 | semidirect |
| 37. #11745169 | C22 | semidirect |
| 38. #11745165 | C22 | semidirect |
| 39. #11745157 | C22 | semidirect |
| 40. #11745155 | C22 | semidirect |
| 80. C8×D29 | D4 | semidirect |
| 139. #470 | D29 | semidirect |
| 155. C2×Q16 | C2×D29 | semidirect |
| 176. #106 | C2×D29 | semidirect |
| 178. #103 | C2×D29 | semidirect |
| 181. C29 | #3054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| C2×M16×D29 | 2 |
| #14271676 | 2 |
| #14271418 | 2 |
| #14271417 | 2 |
| #14271416 | 2 |
| #14271412 | 2 |
| #14271411 | 2 |
| #14271198 | 2 |
| #14271158 | 2 |
| C29×#470 | 2 |
| #3054 | 29 |