Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
396 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 94 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×D20 | C2 | semidirect |
| 2. C3×C5×#121 | C2 | semidirect |
| 3. C2×C3×#686 | C2 | semidirect |
| 4. C3×C22⋊#168 | C2 | semidirect |
| 5. C3×#3941 | C2 | semidirect |
| 6. #65325 | C3 | direct (N × H) |
| 9. C2×C3×C5×D4 | C22 | semidirect |
| 14. C3×C5×C4⋊C4 | C22 | semidirect |
| 17. C2×C3×#168 | C22 | semidirect |
| 19. C22×D20 | C2×C3 | semidirect |
| 20. C5×#121 | C2×C3 | semidirect |
| 21. C2×#686 | C2×C3 | semidirect |
| 22. C22⋊#168 | C2×C3 | semidirect |
| 23. #3941 | C2×C3 | semidirect |
| 38. C3×D20 | D4 | semidirect |
| 42. C3×#121 | D5 | semidirect |
| 47. C2×C5×D4 | C22×C3 | semidirect |
| 52. C5×C4⋊C4 | C22×C3 | semidirect |
| 55. C2×#168 | C22×C3 | semidirect |
| 62. C22×C3×C5 | D8 | semidirect |
| 76. C2×C3×D4 | C2×D5 | semidirect |
| 80. C3×C4⋊C4 | C2×D5 | semidirect |
| 96. D20 | C3×D4 | semidirect |
| 100. #121 | C3×D5 | semidirect |
| 130. C22×C5 | C3×D8 | semidirect |
| 144. C2×D4 | C2×C3×D5 | semidirect |
| 148. C4⋊C4 | C2×C3×D5 | semidirect |
| 150. C3×C5 | #447 | semidirect |
| 160. C22×C3 | #686 | semidirect |
| 193. C5 | C3×#447 | semidirect |
| 203. C22 | C3×#686 | semidirect |
| 208. C3 | #65325 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D20 | 2 |
| C3×C5×#121 | 2 |
| C2×C3×#686 | 2 |
| C3×C22⋊#168 | 2 |
| C3×#3941 | 2 |
| #65325 | 3 |
| C3×#447 | 5 |