Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745364 | C2 | semidirect |
| 2. C22×#90782 | C2 | semidirect |
| 3. #14271730 | C2 | semidirect |
| 4. #14271307 | C2 | semidirect |
| 5. #14271295 | C2 | semidirect |
| 6. #14271169 | C2 | semidirect |
| 7. #14271159 | C2 | semidirect |
| 8. #14271131 | C2 | semidirect |
| 9. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 11. C22×D4×C29 | C22 | semidirect |
| 14. C2×#90809 | C22 | semidirect |
| 16. C2×D4×D29 | C22 | semidirect |
| 22. C2×SD16×C29 | C22 | semidirect |
| 23. C2×D8×C29 | C22 | semidirect |
| 24. C2×M16×C29 | C22 | semidirect |
| 27. #11745300 | C22 | semidirect |
| 30. C2×#90782 | C22 | semidirect |
| 31. #11745288 | C22 | semidirect |
| 32. C22×#6597 | C22 | semidirect |
| 33. #11745183 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745168 | C22 | semidirect |
| 41. #41×C29 | D4 | semidirect |
| 67. C2×D116 | D4 | semidirect |
| 146. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 171. C22×D4 | C2×D29 | semidirect |
| 173. C2×SD16 | C2×D29 | semidirect |
| 176. C2×D8 | C2×D29 | semidirect |
| 177. C2×M16 | C2×D29 | semidirect |
| 188. C29 | #3008 | semidirect |
| 198. #41 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| C22×#90782 | 2 |
| #14271730 | 2 |
| #14271307 | 2 |
| #14271295 | 2 |
| #14271169 | 2 |
| #14271159 | 2 |
| #14271131 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3008 | 29 |