Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14271179 | C2 | semidirect |
| 3. #14271159 | C2 | semidirect |
| 4. #14271131 | C2 | semidirect |
| 5. #14270934 | C2 | semidirect |
| 6. #14270927 | C2 | semidirect |
| 7. C29×#568 | C2 | semidirect |
| 15. #11745313 | C4 | semidirect |
| 17. #11745311 | C4 | semidirect |
| 114. #568 | D29 | semidirect |
| 145. C29 | #1881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271961 | 2 |
| #14271179 | 2 |
| #14271159 | 2 |
| #14271131 | 2 |
| #14270934 | 2 |
| #14270927 | 2 |
| C29×#568 | 2 |
| #1881 | 29 |