Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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×C4×D116 | C2 | semidirect |
| 3. #14271375 | C2 | semidirect |
| 4. #14271365 | C2 | semidirect |
| 5. #14271355 | C2 | semidirect |
| 6. #14271187 | C2 | semidirect |
| 7. #14271164 | C2 | semidirect |
| 8. C29×#532 | C2 | semidirect |
| 12. C29×C4⋊Q8 | C22 | semidirect |
| 13. C29×#127 | C22 | semidirect |
| 14. C29×#124 | C22 | semidirect |
| 30. #11745183 | C22 | semidirect |
| 31. #11745180 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 33. C4⋊#6597 | C22 | semidirect |
| 49. C2×D116 | D4 | semidirect |
| 120. C4×C29 | AGL(1,ℤ/8) | semidirect |
| 125. #532 | D29 | semidirect |
| 145. C4⋊Q8 | C2×D29 | semidirect |
| 146. #127 | C2×D29 | semidirect |
| 147. #124 | C2×D29 | semidirect |
| 163. C29 | #3036 | semidirect |
| 250. C4 | #11745311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C2×C4×D116 | 2 |
| #14271375 | 2 |
| #14271365 | 2 |
| #14271355 | 2 |
| #14271187 | 2 |
| #14271164 | 2 |
| C29×#532 | 2 |
| #3036 | 29 |