Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
612 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#11745215 | C2 | semidirect |
| 2. C2×#11745227 | C2 | semidirect |
| 3. #14272106 | C2 | semidirect |
| 5. C23×C4×C29 | C4 | semidirect |
| 6. C22×C22⋊D29 | C4 | semidirect |
| 12. C22×C4×D29 | C4 | semidirect |
| 14. C22×Dic58 | C4 | semidirect |
| 127. C23×C4 | #1181 | semidirect |
| 132. C29 | #1782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745215 | 2 |
| C2×#11745227 | 2 |
| #14272106 | 2 |
| C22×#90805 | 2 |
| #1782 | 29 |