Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
212 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 100 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. C3×#3996 | C2 | semidirect |
| 4. C3×#3995 | C2 | semidirect |
| 5. D5⋊#108 | C3 | direct (N × H) |
| 19. #3996 | C2×C3 | semidirect |
| 20. #3995 | C2×C3 | semidirect |
| 85. C3×D5 | #108 | semidirect |
| 116. C3×C5 | C2×#108 | semidirect |
| 128. D5 | C3×#108 | semidirect |
| 145. C5 | C2×C3×#108 | semidirect |
| 154. C3 | D5⋊#108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5⋊M16 | 2 |
| C2×C3×C8×D5 | 2 |
| C3×#3996 | 2 |
| C3×#3995 | 2 |
| D5⋊#108 | 3 |
| C2×C3×#108 | 5 |