Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 74 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×C5×Q64 | C2 | semidirect |
| 3. C3×#64742 | C2 | semidirect |
| 4. C3×Dic80 | C2 | semidirect |
| 6. D5×Q64 | C3 | direct (N × H) |
| 16. C5×Q64 | C2×C3 | semidirect |
| 17. #64742 | C2×C3 | semidirect |
| 18. Dic80 | C2×C3 | semidirect |
| 30. C3×Q64 | D5 | direct (N × H) |
| 64. Q64 | C3×D5 | direct (N × H) |
| 93. C3×D5 | Q64 | direct (N × H) |
| 113. C3×C5 | C2×Q64 | semidirect |
| 120. D5 | C3×Q64 | direct (N × H) |
| 130. C5 | C2×C3×Q64 | semidirect |
| 136. C3 | D5×Q64 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×Q32 | 2 |
| C3×C5×Q64 | 2 |
| C3×#64742 | 2 |
| C3×Dic80 | 2 |
| C3×D5×C32 | 2 |
| D5×Q64 | 3 |
| C2×C3×Q64 | 5 |