Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
330 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 16. C4×C5×A4 | C8 | semidirect |
| 56. C22×C4×C5 | C3⋊C8 | semidirect |
| 84. C5×A4 | C4⋊C8 | semidirect |
| 93. C4×A4 | #170 | semidirect |
| 161. C22×C5 | C4⋊(C3⋊C8) | semidirect |
| 164. C4×C5 | A4⋊C8 | semidirect |
| 185. C22×C4 | C3⋊#170 | semidirect |
| 199. A4 | C4⋊#170 | semidirect |
| 244. C5 | C4⋊(A4⋊C8) | semidirect |
| 255. C22 | C4⋊(C3⋊#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 |
| #10604899 | 3 |
| C4⋊(C3⋊#170) | 4 |
| C4⋊(A4⋊C8) | 5 |