Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
596 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 210 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. C22×C3×#170 | C2 | semidirect |
| 4. C2×#6740 | C2 | direct (N × H) |
| 11. C2×C3⋊#170 | C22 | semidirect |
| 12. C2×C3×#170 | C22 | semidirect |
| 13. #6740 | C22 | direct (N × H) |
| 17. C22×#170 | D3 | semidirect |
| 27. C3⋊#170 | C23 | semidirect |
| 28. C3×#170 | C23 | semidirect |
| 39. C2×#170 | C2×D3 | semidirect |
| 42. C22×C3×C5 | M16 | semidirect |
| 66. #170 | C22×D3 | semidirect |
| 71. C2×C3×C5 | C2×M16 | semidirect |
| 84. C22×C5 | ΓL(1,𝔽25) | semidirect |
| 99. C3×C5 | C22×M16 | semidirect |
| 100. C22×C3 | #700 | semidirect |
| 107. C2×C5 | C2×ΓL(1,𝔽25) | semidirect |
| 120. C2×C3 | C2×#700 | semidirect |
| 123. C5 | C22×ΓL(1,𝔽25) | semidirect |
| 126. C22 | #6740 | direct (N × H) |
| 131. C3 | C22×#700 | semidirect |
| 133. C2 | C2×#6740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1200 | 2 |
| C22×C3⋊#170 | 2 |
| C22×C3×#170 | 2 |
| C2×#6740 | 2 |
| C22×#700 | 3 |
| C22×ΓL(1,𝔽25) | 5 |