Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
268 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 1. C22×C3×#170 | C2 | semidirect |
| 3. C3×C22⋊#170 | C2 | semidirect |
| 4. C3×C4⋊#170 | C2 | semidirect |
| 5. C3×C4×#170 | C2 | semidirect |
| 6. D4×#170 | C3 | direct (N × H) |
| 17. C22×#170 | C2×C3 | semidirect |
| 19. C22⋊#170 | C2×C3 | semidirect |
| 20. C4⋊#170 | C2×C3 | semidirect |
| 21. C4×#170 | C2×C3 | semidirect |
| 23. C3×C5×D4 | C8 | semidirect |
| 32. C3×#170 | D4 | direct (N × H) |
| 50. C22×C3×C5 | C2×C8 | semidirect |
| 52. C3×C4×C5 | C2×C8 | semidirect |
| 67. C5×D4 | C3×C8 | semidirect |
| 76. #170 | C3×D4 | direct (N × H) |
| 87. C3×D4 | #170 | direct (N × H) |
| 99. C22×C5 | C2×C3×C8 | semidirect |
| 101. C4×C5 | C2×C3×C8 | semidirect |
| 115. C3×C5 | C8×D4 | semidirect |
| 118. C22×C3 | C2×#170 | semidirect |
| 124. C3×C4 | C2×#170 | semidirect |
| 130. D4 | C3×#170 | direct (N × H) |
| 144. C5 | C3×C8×D4 | semidirect |
| 147. C22 | C2×C3×#170 | semidirect |
| 153. C4 | C2×C3×#170 | semidirect |
| 154. C3 | D4×#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#170 | 2 |
| C3×D4×Dic5 | 2 |
| C3×C22⋊#170 | 2 |
| C3×C4⋊#170 | 2 |
| C3×C4×#170 | 2 |
| D4×#170 | 3 |
| C3×C8×D4 | 5 |