Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#11745313 | C2 | semidirect |
| 2. C2×#11745298 | C2 | semidirect |
| 3. #41×Dic29 | C2 | semidirect |
| 4. #14271383 | C2 | semidirect |
| 5. #14271376 | C2 | semidirect |
| 6. #14271186 | C2 | semidirect |
| 7. #14271173 | C2 | semidirect |
| 8. #14271168 | C2 | semidirect |
| 19. Q8×Dic29 | C22 | semidirect |
| 20. C2×#90785 | C22 | semidirect |
| 25. D4×Dic29 | C22 | semidirect |
| 26. C2×#90783 | C22 | semidirect |
| 33. #11745164 | C22 | semidirect |
| 34. #11745162 | C22 | semidirect |
| 160. C29 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C2×#11745298 | 2 |
| #41×Dic29 | 2 |
| #14271383 | 2 |
| #14271376 | 2 |
| #14271186 | 2 |
| #14271173 | 2 |
| #14271168 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3040 | 29 |