Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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. C22×D232 | C2 | semidirect |
| 2. C2×D464 | C2 | semidirect |
| 3. #14271399 | C2 | semidirect |
| 4. #14270965 | C2 | semidirect |
| 5. C29×C22⋊C16 | C2 | semidirect |
| 12. C2×D232 | C22 | semidirect |
| 13. C2×C16×C29 | C22 | semidirect |
| 15. #11745166 | C22 | semidirect |
| 33. D232 | D4 | semidirect |
| 57. C22×C29 | D16 | semidirect |
| 74. C22⋊C16 | D29 | semidirect |
| 89. C2×C16 | C2×D29 | semidirect |
| 92. C29 | #2184 | semidirect |
| 139. C22 | D464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C2×D464 | 2 |
| #14271399 | 2 |
| #14270965 | 2 |
| C29×C22⋊C16 | 2 |
| #2184 | 29 |