Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C3×#4033 | C2 | semidirect |
| 4. C3×C5×#107 | C2 | semidirect |
| 5. C3×#3947 | C2 | semidirect |
| 6. C3×#3942 | C2 | semidirect |
| 8. #65178 | C3 | direct (N × H) |
| 20. C3×#677 | C4 | semidirect |
| 24. #4033 | C2×C3 | semidirect |
| 25. C5×#107 | C2×C3 | semidirect |
| 26. #3947 | C2×C3 | semidirect |
| 27. #3942 | C2×C3 | semidirect |
| 40. C3×Dic10 | C2×C4 | semidirect |
| 41. C3×C5×C8 | C2×C4 | semidirect |
| 46. C3×#107 | D5 | semidirect |
| 61. #677 | C3×C4 | semidirect |
| 97. Dic10 | C2×C3×C4 | semidirect |
| 98. C5×C8 | C2×C3×C4 | semidirect |
| 103. #107 | C3×D5 | semidirect |
| 124. C3×C8 | C4×D5 | semidirect |
| 148. C3×C5 | #440 | semidirect |
| 177. C8 | C3×C4×D5 | semidirect |
| 182. C5 | C3×#440 | semidirect |
| 194. C3 | #65178 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#677 | 2 |
| C3×#4039 | 2 |
| C3×#4033 | 2 |
| C3×C5×#107 | 2 |
| C3×#3947 | 2 |
| C3×#3942 | 2 |
| C3×#3941 | 2 |
| #65178 | 3 |
| C3×#440 | 5 |