Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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. #14271961 | C2 | semidirect |
| 2. #14271737 | C2 | semidirect |
| 3. #14271346 | C2 | semidirect |
| 4. #14271336 | C2 | semidirect |
| 5. #14271180 | C2 | semidirect |
| 6. C2×#11745184 | C2 | semidirect |
| 7. C2×C29×2−1+4 | C2 | semidirect |
| 17. #11745313 | C22 | semidirect |
| 19. #11745311 | C22 | semidirect |
| 20. #11745309 | C22 | semidirect |
| 22. #11745306 | C22 | semidirect |
| 28. #11745185 | C22 | semidirect |
| 29. #11745184 | C22 | semidirect |
| 118. C2×2−1+4 | D29 | semidirect |
| 153. C29 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271961 | 2 |
| #14271737 | 2 |
| #14271346 | 2 |
| #14271336 | 2 |
| #14271180 | 2 |
| C2×#11745184 | 2 |
| C2×C29×2−1+4 | 2 |
| #3020 | 29 |