Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 92 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. C3×C4⋊#674 | C2 | semidirect |
| 3. C3×C4×#674 | C2 | semidirect |
| 4. D4⋊#674 | C3 | direct (N × H) |
| 14. C4⋊#674 | C2×C3 | semidirect |
| 15. C4×#674 | C2×C3 | semidirect |
| 41. C3×C5×D4 | C16 | semidirect |
| 98. C5×D4 | C3×C16 | semidirect |
| 122. C3×D4 | #674 | semidirect |
| 155. C3×C5 | D4⋊C16 | semidirect |
| 172. D4 | C3×#674 | semidirect |
| 187. C5 | C3×D4⋊C16 | semidirect |
| 198. C3 | D4⋊#674 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×#168 | 2 |
| C3×C4⋊#674 | 2 |
| C3×C4×#674 | 2 |
| D4⋊#674 | 3 |
| C3×D4⋊C16 | 5 |