Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 2. C5×Q8×Dic3 | C2 | semidirect |
| 4. C3×#3967 | C2 | semidirect |
| 5. #90989 | C2 | semidirect |
| 7. #90953 | C2 | semidirect |
| 12. #6717 | C4 | semidirect |
| 25. #3967 | D3 | semidirect |
| 31. C3×C5×Q8 | C2×C4 | semidirect |
| 41. C3⋊#168 | C2×C4 | semidirect |
| 43. Q8×Dic3 | D5 | semidirect |
| 88. C5×Q8 | C4×D3 | semidirect |
| 113. C3×Q8 | C4×D5 | semidirect |
| 148. C3×C5 | #440 | semidirect |
| 166. Q8 | #1200 | semidirect |
| 182. C5 | #4817 | semidirect |
| 194. C3 | #65315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6717 | 2 |
| C5×Q8×Dic3 | 2 |
| #91428 | 2 |
| C3×#3967 | 2 |
| #90989 | 2 |
| #90969 | 2 |
| #90953 | 2 |
| #65315 | 3 |
| #4817 | 5 |