Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#11745269 | C2 | semidirect |
| 2. #14271741 | C2 | semidirect |
| 3. #14271730 | C2 | semidirect |
| 4. #14271413 | C2 | semidirect |
| 5. #14271406 | C2 | semidirect |
| 6. #14271396 | C2 | semidirect |
| 7. #14271389 | C2 | semidirect |
| 8. #14271205 | C2 | semidirect |
| 9. #14271159 | C2 | semidirect |
| 10. C2×#11745180 | C2 | semidirect |
| 11. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 20. #11745308 | C22 | semidirect |
| 25. #11745300 | C22 | semidirect |
| 33. C2×#90772 | C22 | semidirect |
| 34. C2×C8×D29 | C22 | semidirect |
| 35. #11745183 | C22 | semidirect |
| 36. #11745183 | C22 | semidirect |
| 39. #11745180 | C22 | semidirect |
| 40. #11745180 | C22 | semidirect |
| 41. #11745166 | C22 | semidirect |
| 42. #11745165 | C22 | semidirect |
| 67. M16×C29 | D4 | semidirect |
| 145. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 194. C29 | #3062 | semidirect |
| 220. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745269 | 2 |
| #14271741 | 2 |
| #14271730 | 2 |
| #14271413 | 2 |
| #14271406 | 2 |
| #14271396 | 2 |
| #14271389 | 2 |
| #14271205 | 2 |
| #14271159 | 2 |
| C2×#11745180 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3062 | 29 |