Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. C3×#4004 | C2 | semidirect |
| 5. C3×C4⋊#170 | C2 | semidirect |
| 6. #65696 | C3 | direct (N × H) |
| 21. #4004 | C2×C3 | semidirect |
| 22. C4⋊#170 | C2×C3 | semidirect |
| 113. C3×C5 | #424 | semidirect |
| 138. C5 | C3×#424 | semidirect |
| 147. C3 | #65696 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#704 | 2 |
| C22×C3×#170 | 2 |
| C3×#4023 | 2 |
| C3×#4004 | 2 |
| C3×C4⋊#170 | 2 |
| #65696 | 3 |
| C3×#424 | 5 |