Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. #100×D29 | C2 | semidirect |
| 3. #99×D29 | C2 | semidirect |
| 4. #14270954 | C2 | semidirect |
| 5. #14270952 | C2 | semidirect |
| 6. #14270950 | C2 | semidirect |
| 7. C29×AΣL(1,𝔽16) | C2 | semidirect |
| 8. C22×C22⋊D29 | C4 | semidirect |
| 11. #11745315 | C4 | semidirect |
| 16. #11745248 | C4 | semidirect |
| 20. C22⋊C4×D29 | C4 | semidirect |
| 27. C24×C29 | C2×C4 | semidirect |
| 39. C22×Dic29 | C2×C4 | semidirect |
| 49. C22⋊C4×C29 | C2×C4 | semidirect |
| 53. C22⋊Dic29 | C2×C4 | semidirect |
| 133. AΣL(1,𝔽16) | D29 | semidirect |
| 162. C29 | #2121 | semidirect |
| 165. C24 | C4×D29 | semidirect |
| 197. C22⋊C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271723 | 2 |
| #100×D29 | 2 |
| #99×D29 | 2 |
| #14270954 | 2 |
| #14270952 | 2 |
| #14270950 | 2 |
| C29×AΣL(1,𝔽16) | 2 |
| #2121 | 29 |