Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #14271930 | C2 | semidirect |
| 2. #14271180 | C2 | semidirect |
| 3. #14271159 | C2 | semidirect |
| 4. #14271130 | C2 | semidirect |
| 5. #14270935 | C2 | semidirect |
| 6. #14270927 | C2 | semidirect |
| 11. C29×#137 | C4 | semidirect |
| 13. C29×AGL(1,ℤ/8) | C4 | semidirect |
| 129. #137 | Dic29 | semidirect |
| 131. AGL(1,ℤ/8) | Dic29 | semidirect |
| 145. C29 | #1881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271930 | 2 |
| #14271180 | 2 |
| #14271159 | 2 |
| #14271130 | 2 |
| #14270935 | 2 |
| #14270927 | 2 |
| C29×#575 | 2 |
| #1881 | 29 |