Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
| 4. C3×#3967 | C2 | semidirect |
| 6. C3×#3940 | C2 | semidirect |
| 7. C3×C4×#168 | C2 | semidirect |
| 8. C4×#688 | C3 | direct (N × H) |
| 16. C3×#688 | C4 | direct (N × H) |
| 22. C4×C5×Q8 | C2×C3 | semidirect |
| 25. #3967 | C2×C3 | semidirect |
| 27. #3940 | C2×C3 | semidirect |
| 28. C4×#168 | C2×C3 | semidirect |
| 31. C3×C5×Q8 | C2×C4 | semidirect |
| 42. C3×#168 | C2×C4 | semidirect |
| 44. C3×C4×Q8 | D5 | semidirect |
| 57. #688 | C3×C4 | direct (N × H) |
| 70. C3×C4×C5 | SD16 | semidirect |
| 88. C5×Q8 | C2×C3×C4 | semidirect |
| 99. #168 | C2×C3×C4 | semidirect |
| 101. C4×Q8 | C3×D5 | semidirect |
| 113. C3×Q8 | C4×D5 | semidirect |
| 132. C4×C5 | C3×SD16 | semidirect |
| 148. C3×C5 | C4×SD16 | semidirect |
| 157. C3×C4 | #688 | direct (N × H) |
| 166. Q8 | C3×C4×D5 | semidirect |
| 182. C5 | C3×C4×SD16 | semidirect |
| 191. C4 | C3×#688 | direct (N × H) |
| 194. C3 | C4×#688 | 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×#688 | 2 |
| C3×C4×D20 | 2 |
| C3×#3967 | 2 |
| C3×#3941 | 2 |
| C3×#3940 | 2 |
| C3×C4×#168 | 2 |
| C4×#688 | 3 |
| C3×C4×SD16 | 5 |