Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11746720 | C2 | semidirect |
| 4. C3×#64849 | C2 | semidirect |
| 5. #11746476 | C2 | semidirect |
| 12. C16×D15 | C4 | semidirect |
| 13. C5×D3×C16 | C4 | semidirect |
| 15. #90933 | C4 | semidirect |
| 16. D3×#672 | C4 | semidirect |
| 23. #64849 | D3 | direct (N × H) |
| 35. C3×C5×C16 | C2×C4 | semidirect |
| 36. C3⋊#672 | C2×C4 | semidirect |
| 37. C3×#672 | C2×C4 | semidirect |
| 38. C5×C3⋊C16 | C2×C4 | semidirect |
| 80. D3×C16 | AGL(1,𝔽5) | semidirect |
| 93. C5×C16 | C4×D3 | semidirect |
| 95. #672 | C4×D3 | semidirect |
| 124. C3×C16 | C2×AGL(1,𝔽5) | semidirect |
| 126. C3⋊C16 | C2×AGL(1,𝔽5) | semidirect |
| 153. D15 | #366 | semidirect |
| 156. C5×D3 | #366 | semidirect |
| 196. C16 | D3×AGL(1,𝔽5) | semidirect |
| 197. C3×C5 | C2×#366 | semidirect |
| 232. D3 | #64849 | direct (N × H) |
| 233. C5 | D3×#366 | semidirect |
| 245. C3 | C2×#64849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#3994 | 2 |
| D3×D5×C16 | 2 |
| #11746720 | 2 |
| C3×#64849 | 2 |
| #11746476 | 2 |
| C2×#64849 | 3 |
| D3×#366 | 5 |