Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
236 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 4. C3×#3994 | C2 | semidirect |
| 5. C3×#3993 | C2 | semidirect |
| 6. #65727 | C3 | direct (N × H) |
| 15. C3×C5×M16 | C4 | semidirect |
| 16. C3×#681 | C4 | semidirect |
| 17. C3×#676 | C4 | semidirect |
| 23. #3994 | C2×C3 | semidirect |
| 24. #3993 | C2×C3 | semidirect |
| 36. C3×C5×C8 | C2×C4 | semidirect |
| 37. C3×#168 | C2×C4 | semidirect |
| 51. C5×M16 | C3×C4 | semidirect |
| 52. #681 | C3×C4 | semidirect |
| 53. #676 | C3×C4 | semidirect |
| 72. C3×M16 | AGL(1,𝔽5) | semidirect |
| 91. C5×C8 | C2×C3×C4 | semidirect |
| 92. #168 | C2×C3×C4 | semidirect |
| 115. C3×C8 | C2×AGL(1,𝔽5) | semidirect |
| 132. M16 | C3×AGL(1,𝔽5) | semidirect |
| 140. C3×C5 | #428 | semidirect |
| 170. C8 | C2×C3×AGL(1,𝔽5) | semidirect |
| 176. C5 | C3×#428 | semidirect |
| 189. C3 | #65727 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4130 | 2 |
| C2×C3×C4⋊AGL(1,𝔽5) | 2 |
| C3×D5×M16 | 2 |
| C3×#3994 | 2 |
| C3×#3993 | 2 |
| #65727 | 3 |
| C3×#428 | 5 |