Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
224 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 224 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×Q8 | C2 | semidirect |
| 2. C2×C3×#689 | C2 | semidirect |
| 5. C3×#3942 | C2 | semidirect |
| 7. C3×C4⋊#168 | C2 | semidirect |
| 8. #65317 | C3 | direct (N × H) |
| 23. C4×C5×Q8 | C2×C3 | semidirect |
| 24. C2×#689 | C2×C3 | semidirect |
| 27. #3942 | C2×C3 | semidirect |
| 29. C4⋊#168 | C2×C3 | semidirect |
| 48. C3×C4×Q8 | D5 | semidirect |
| 108. C4×Q8 | C3×D5 | semidirect |
| 155. C3×C5 | #464 | semidirect |
| 190. C5 | C3×#464 | semidirect |
| 202. C3 | #65317 | 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×Q8 | 2 |
| C2×C3×#689 | 2 |
| C2×C3×#688 | 2 |
| C3×#4021 | 2 |
| C3×#3942 | 2 |
| C3×#3941 | 2 |
| C3×C4⋊#168 | 2 |
| #65317 | 3 |
| C3×#464 | 5 |