Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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×D464 | C2 | semidirect |
| 2. #14271540 | C2 | semidirect |
| 3. C4×D232 | C2 | semidirect |
| 4. #14270965 | C2 | semidirect |
| 5. C29×C4⋊C16 | C2 | semidirect |
| 30. D232 | D4 | semidirect |
| 57. C4×C29 | D16 | semidirect |
| 64. C4⋊C16 | D29 | semidirect |
| 81. C29 | #2206 | semidirect |
| 123. C4 | D464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D464 | 2 |
| #14271540 | 2 |
| C4×D232 | 2 |
| #14270965 | 2 |
| C29×C4⋊C16 | 2 |
| #2206 | 29 |