Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14271203 | C2 | semidirect |
| 5. #14270924 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#428 | C2 | semidirect |
| 23. #11745171 | C4 | semidirect |
| 39. M16×C29 | C2×C4 | semidirect |
| 57. #90777 | C2×C4 | semidirect |
| 111. #428 | D29 | semidirect |
| 140. C29 | #1856 | semidirect |
| 156. M16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271637 | 2 |
| #14271203 | 2 |
| C2×#11745171 | 2 |
| #14271064 | 2 |
| #14270924 | 2 |
| #14270922 | 2 |
| C29×#428 | 2 |
| #1856 | 29 |