Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 324 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×#713 | C2 | semidirect |
| 2. C2×C3×C5×SD16 | C2 | semidirect |
| 3. C3×#4084 | C2 | semidirect |
| 4. C2×C3×#686 | C2 | semidirect |
| 5. C3×#3967 | C2 | semidirect |
| 6. C3×#3953 | C2 | semidirect |
| 7. C3×#3952 | C2 | semidirect |
| 8. #65461 | C3 | direct (N × H) |
| 25. C2×#713 | C2×C3 | semidirect |
| 26. C2×C5×SD16 | C2×C3 | semidirect |
| 27. #4084 | C2×C3 | semidirect |
| 28. C2×#686 | C2×C3 | semidirect |
| 29. #3967 | C2×C3 | semidirect |
| 30. #3953 | C2×C3 | semidirect |
| 31. #3952 | C2×C3 | semidirect |
| 36. C3×C5×Q8 | D4 | semidirect |
| 46. C3×D20 | D4 | semidirect |
| 53. C2×C3×SD16 | D5 | semidirect |
| 109. C5×Q8 | C3×D4 | semidirect |
| 119. D20 | C3×D4 | semidirect |
| 126. C2×SD16 | C3×D5 | semidirect |
| 142. C3×Q8 | C22⋊D5 | semidirect |
| 188. C3×C5 | #449 | semidirect |
| 214. Q8 | C3×C22⋊D5 | semidirect |
| 236. C5 | C3×#449 | semidirect |
| 252. C3 | #65461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#713 | 2 |
| C2×C3×C5×SD16 | 2 |
| C3×#4084 | 2 |
| C2×C3×#686 | 2 |
| C3×#3967 | 2 |
| C3×#3953 | 2 |
| C3×#3952 | 2 |
| #65461 | 3 |
| C3×#449 | 5 |