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. C2×C3×C5×Q16 | C2 | semidirect |
| 3. C3×#4090 | C2 | semidirect |
| 4. C2×C3×#689 | C2 | semidirect |
| 7. C3×#3947 | C2 | semidirect |
| 8. #65479 | C3 | direct (N × H) |
| 23. C2×C5×Q16 | C2×C3 | semidirect |
| 25. #4090 | C2×C3 | semidirect |
| 26. C2×#689 | C2×C3 | semidirect |
| 29. #3947 | C2×C3 | semidirect |
| 47. C2×C3×Q16 | D5 | semidirect |
| 106. C2×Q16 | C3×D5 | semidirect |
| 153. C3×C5 | #497 | semidirect |
| 185. C5 | C3×#497 | semidirect |
| 195. C3 | #65479 | 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×Q16 | 2 |
| C3×#4093 | 2 |
| C3×#4090 | 2 |
| C2×C3×#689 | 2 |
| C2×C3×#688 | 2 |
| C2×C3×#677 | 2 |
| C3×#3947 | 2 |
| #65479 | 3 |
| C3×#497 | 5 |