Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 72 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. C22×C4⋊#170 | C3 | semidirect |
| 16. C4×C5×A4 | C8 | semidirect |
| 38. C4⋊#170 | A4 | direct (N × H) |
| 56. C22×C4×C5 | C3×C8 | semidirect |
| 84. C5×A4 | C4⋊C8 | semidirect |
| 93. C4×A4 | #170 | semidirect |
| 161. C22×C5 | C3×C4⋊C8 | semidirect |
| 164. C4×C5 | C8×A4 | semidirect |
| 185. C22×C4 | C3×#170 | semidirect |
| 199. A4 | C4⋊#170 | direct (N × H) |
| 244. C5 | A4×C4⋊C8 | semidirect |
| 255. C22 | C3×C4⋊#170 | semidirect |
| 264. C4 | A4×#170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×#170 | 2 |
| C4×A4×Dic5 | 2 |
| C22×C4⋊#170 | 3 |
| C3×C4⋊#170 | 4 |
| A4×C4⋊C8 | 5 |