Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 248 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. C3×C4×C5×D4 | C2 | semidirect |
| 2. C2×C3×#687 | C2 | semidirect |
| 4. C3×#4021 | C2 | semidirect |
| 5. C3×#3942 | C2 | semidirect |
| 6. C3×#3941 | C2 | semidirect |
| 7. C3×C4⋊#168 | C2 | semidirect |
| 8. #65305 | C3 | direct (N × H) |
| 23. C4×C5×D4 | C2×C3 | semidirect |
| 24. C2×#687 | C2×C3 | semidirect |
| 26. #4021 | C2×C3 | semidirect |
| 27. #3942 | C2×C3 | semidirect |
| 28. #3941 | C2×C3 | semidirect |
| 29. C4⋊#168 | C2×C3 | semidirect |
| 49. C3×C4×D4 | D5 | semidirect |
| 112. C4×D4 | C3×D5 | semidirect |
| 163. C3×C5 | #463 | semidirect |
| 203. C5 | C3×#463 | semidirect |
| 217. C3 | #65305 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×D4 | 2 |
| C2×C3×#687 | 2 |
| C2×C3×#686 | 2 |
| C3×#4021 | 2 |
| C3×#3942 | 2 |
| C3×#3941 | 2 |
| C3×C4⋊#168 | 2 |
| #65305 | 3 |
| C3×#463 | 5 |