Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
196 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 3. C5×#2863 | C3 | semidirect |
| 6. #2863⋊C3 | C5 | direct (N × H) |
| 14. C5×C42⋊C3 | Q8 | semidirect |
| 26. #2863 | C3×C5 | semidirect |
| 45. C42×C5 | C3×Q8 | semidirect |
| 56. C42⋊C3 | C5×Q8 | semidirect |
| 108. C42 | C3×C5×Q8 | semidirect |
| 132. C5 | #2863⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#383⋊C3 | 2 |
| C4×C5×C42⋊C3 | 2 |
| C5×#2863 | 3 |
| C5×Q8×A4 | 4 |
| #2863⋊C3 | 5 |