Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
820 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#11745171 | C2 | semidirect |
| 3. #14271127 | C2 | semidirect |
| 4. C29×#407 | C2 | semidirect |
| 12. C2×M16×C29 | C22 | semidirect |
| 13. C2×#90777 | C22 | semidirect |
| 68. C22×C29 | #100 | semidirect |
| 82. #407 | D29 | semidirect |
| 96. C2×M16 | C2×D29 | semidirect |
| 100. C29 | #1783 | semidirect |
| 156. C22 | #11745171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C2×#11745171 | 2 |
| #14271127 | 2 |
| C29×#407 | 2 |
| #1783 | 29 |