Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 2. C2×C3×#700 | C2 | semidirect |
| 3. C2×C3×D5⋊C8 | C2 | semidirect |
| 4. C3×#4003 | C2 | semidirect |
| 5. #65787 | C3 | direct (N × H) |
| 19. C2×#700 | C2×C3 | semidirect |
| 20. C2×D5⋊C8 | C2×C3 | semidirect |
| 21. #4003 | C2×C3 | semidirect |
| 128. C3×C5 | #408 | semidirect |
| 160. C5 | C3×#408 | semidirect |
| 170. C3 | #65787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#713 | 2 |
| C2×C3×#700 | 2 |
| C2×C3×D5⋊C8 | 2 |
| C3×#4003 | 2 |
| #65787 | 3 |
| C3×#408 | 5 |