Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
340 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#6710 | C2 | semidirect |
| 3. C2×C4×C5×Dic3 | C2 | semidirect |
| 4. #90977 | C2 | direct (N × H) |
| 11. C3×#709 | C4 | semidirect |
| 13. C2×C3×D20 | C4 | semidirect |
| 15. C2×C3×Dic10 | C4 | semidirect |
| 17. #6710 | C22 | semidirect |
| 20. C4×C5×Dic3 | C22 | semidirect |
| 40. C3×D20 | C2×C4 | semidirect |
| 44. C3×Dic10 | C2×C4 | semidirect |
| 47. C2×C4×Dic3 | D5 | semidirect |
| 55. #709 | Dic3 | semidirect |
| 57. C2×D20 | Dic3 | semidirect |
| 59. C2×Dic10 | Dic3 | semidirect |
| 89. C4×Dic3 | C2×D5 | semidirect |
| 107. D20 | C2×Dic3 | semidirect |
| 111. Dic10 | C2×Dic3 | semidirect |
| 119. C2×C3×C5 | #104 | semidirect |
| 169. C3×C5 | C2×#104 | semidirect |
| 184. C2×C5 | #837 | semidirect |
| 210. C2×C3 | #3937 | semidirect |
| 212. C5 | C2×#837 | semidirect |
| 225. C3 | C2×#3937 | semidirect |
| 229. C2 | #90977 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#709 | 2 |
| C2×#6710 | 2 |
| C2×C4×C5×Dic3 | 2 |
| #90977 | 2 |
| C2×#3937 | 3 |
| C2×#837 | 5 |