Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
600 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 316 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. #10604190 | C3 | direct (N × H) |
| 16. C3×C42×C5 | C8 | semidirect |
| 46. C42×C5 | C3×C8 | semidirect |
| 55. C3×C4×C5 | C4⋊C8 | semidirect |
| 66. C3×C42 | #170 | semidirect |
| 96. C4×C5 | C3×C4⋊C8 | semidirect |
| 107. C42 | C3×#170 | semidirect |
| 108. C3×C5 | #1842 | semidirect |
| 115. C3×C4 | C4⋊#170 | semidirect |
| 131. C5 | C3×#1842 | semidirect |
| 138. C4 | C3×C4⋊#170 | semidirect |
| 139. C3 | #10604190 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊#170 | 2 |
| C3×C42×Dic5 | 2 |
| #10604190 | 3 |
| C3×#1842 | 5 |