Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#90782 | C2 | semidirect |
| 2. #14271727 | C2 | semidirect |
| 3. #14271638 | C2 | semidirect |
| 4. #14271380 | C2 | semidirect |
| 5. #14271356 | C2 | semidirect |
| 6. #14271191 | C2 | semidirect |
| 7. #14271169 | C2 | semidirect |
| 8. #14271159 | C2 | semidirect |
| 9. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 14. C2×SD16×C29 | C22 | semidirect |
| 15. C2×D8×C29 | C22 | semidirect |
| 18. #11745309 | C22 | semidirect |
| 19. #11745302 | C22 | semidirect |
| 22. D4×Dic29 | C22 | semidirect |
| 29. #11745183 | C22 | semidirect |
| 30. #11745180 | C22 | semidirect |
| 31. #11745169 | C22 | semidirect |
| 32. #11745162 | C22 | semidirect |
| 41. C2×D4×C29 | D4 | semidirect |
| 116. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 135. C2×SD16 | C2×D29 | semidirect |
| 138. C2×D8 | C2×D29 | semidirect |
| 154. C29 | #3041 | semidirect |
| 168. C2×D4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90782 | 2 |
| #14271727 | 2 |
| #14271638 | 2 |
| #14271380 | 2 |
| #14271356 | 2 |
| #14271191 | 2 |
| #14271169 | 2 |
| #14271159 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3041 | 29 |