Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 178 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. C22×C3⋊#170 | C2 | semidirect |
| 3. C2×C3×#704 | C2 | semidirect |
| 4. C2×#6740 | C2 | semidirect |
| 5. C2×#6739 | C2 | semidirect |
| 6. C2×#6738 | C2 | semidirect |
| 7. #91929 | C2 | direct (N × H) |
| 8. C2×D3×#170 | C2 | semidirect |
| 21. C2×C3⋊#170 | C22 | semidirect |
| 22. C3×#704 | C22 | semidirect |
| 25. #6740 | C22 | semidirect |
| 26. #6739 | C22 | semidirect |
| 27. #6738 | C22 | semidirect |
| 28. D3×#170 | C22 | semidirect |
| 32. C2×#704 | D3 | semidirect |
| 77. #704 | C2×D3 | semidirect |
| 148. C2×C3×C5 | #131 | semidirect |
| 204. C3×C5 | C2×#131 | semidirect |
| 219. C2×C5 | #907 | semidirect |
| 244. C2×C3 | #4131 | semidirect |
| 248. C5 | C2×#907 | semidirect |
| 261. C3 | C2×#4131 | semidirect |
| 265. C2 | #91929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6782 | 2 |
| C22×C3⋊#170 | 2 |
| C2×C3×#704 | 2 |
| C2×#6740 | 2 |
| C2×#6739 | 2 |
| C2×#6738 | 2 |
| #91929 | 2 |
| C2×D3×#170 | 2 |
| C2×#4131 | 3 |
| C2×#907 | 5 |