Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
584 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11745311 | C2 | semidirect |
| 2. C2×#11745302 | C2 | semidirect |
| 3. #41×Dic29 | C2 | semidirect |
| 4. #14271361 | C2 | semidirect |
| 5. #14271356 | C2 | semidirect |
| 6. #14271186 | C2 | semidirect |
| 7. #14271169 | C2 | semidirect |
| 8. #14271168 | C2 | semidirect |
| 9. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 15. C2×SD16×C29 | C22 | semidirect |
| 16. C2×D8×C29 | C22 | semidirect |
| 19. Q8×Dic29 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 25. D4×Dic29 | C22 | semidirect |
| 26. C2×#90782 | C22 | semidirect |
| 32. #11745180 | C22 | semidirect |
| 33. #11745169 | C22 | semidirect |
| 34. #11745162 | C22 | semidirect |
| 38. #41×C29 | D4 | semidirect |
| 83. Q8×C29 | C2×D4 | semidirect |
| 89. D4×C29 | C2×D4 | semidirect |
| 126. Dic29 | AGL(1,ℤ/8) | semidirect |
| 128. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 149. C2×SD16 | C2×D29 | semidirect |
| 151. C2×D8 | C2×D29 | semidirect |
| 167. C29 | #3038 | semidirect |
| 171. #41 | C22⋊D29 | semidirect |
| 216. Q8 | C2×C22⋊D29 | semidirect |
| 227. D4 | C2×C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C2×#11745302 | 2 |
| #41×Dic29 | 2 |
| #14271361 | 2 |
| #14271356 | 2 |
| #14271186 | 2 |
| #14271169 | 2 |
| #14271168 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3038 | 29 |