Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
596 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 194 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×#6758 | C2 | semidirect |
| 3. C2×C3×#700 | C2 | semidirect |
| 4. C2×#6740 | C2 | semidirect |
| 5. C2×D3×#170 | C2 | semidirect |
| 6. D3×#700 | C2 | direct (N × H) |
| 17. C2×C3⋊#170 | C22 | semidirect |
| 18. #6758 | C22 | semidirect |
| 19. C2×C3×#170 | C22 | semidirect |
| 20. C3×#700 | C22 | semidirect |
| 21. #6740 | C22 | semidirect |
| 22. D3×#170 | C22 | semidirect |
| 29. C2×#700 | D3 | direct (N × H) |
| 48. C3⋊#170 | C23 | semidirect |
| 49. C3×#170 | C23 | semidirect |
| 67. C2×#170 | C2×D3 | semidirect |
| 70. #700 | C2×D3 | direct (N × H) |
| 75. C2×C5×D3 | M16 | semidirect |
| 119. #170 | C22×D3 | semidirect |
| 126. C2×C3×C5 | C2×M16 | semidirect |
| 130. C5×D3 | C2×M16 | semidirect |
| 179. C3×C5 | C22×M16 | semidirect |
| 186. C2×D3 | #700 | direct (N × H) |
| 194. C2×C5 | D3×M16 | semidirect |
| 219. C2×C3 | C2×#700 | semidirect |
| 222. D3 | C2×#700 | direct (N × H) |
| 223. C5 | C2×D3×M16 | semidirect |
| 237. C3 | C22×#700 | semidirect |
| 241. C2 | D3×#700 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×D5 | 2 |
| C2×#6758 | 2 |
| C2×C3×#700 | 2 |
| C2×#6740 | 2 |
| C2×D3×#170 | 2 |
| D3×#700 | 2 |
| C22×#700 | 3 |
| C2×D3×M16 | 5 |