Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×C5×C4⋊C4 | C2 | semidirect |
| 3. C3×C22⋊#168 | C2 | semidirect |
| 4. C3×#3941 | C2 | semidirect |
| 5. C3×#3940 | C2 | semidirect |
| 6. #65257 | C3 | direct (N × H) |
| 17. C2×C5×C4⋊C4 | C2×C3 | semidirect |
| 19. C22⋊#168 | C2×C3 | semidirect |
| 20. #3941 | C2×C3 | semidirect |
| 21. #3940 | C2×C3 | semidirect |
| 34. C2×C3×C4⋊C4 | D5 | semidirect |
| 80. C2×C4⋊C4 | C3×D5 | semidirect |
| 120. C3×C5 | #481 | semidirect |
| 153. C5 | C3×#481 | semidirect |
| 165. C3 | #65257 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×C4⋊C4 | 2 |
| C3×#4076 | 2 |
| C3×C22⋊#168 | 2 |
| C3×#3941 | 2 |
| C3×#3940 | 2 |
| #65257 | 3 |
| C3×#481 | 5 |