Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
268 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 92 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×C8×D15 | C2 | semidirect |
| 2. C2×C3×C8×D5 | C2 | semidirect |
| 4. C5×C8×Dic3 | C2 | semidirect |
| 5. Dic3⋊#168 | C2 | semidirect |
| 6. #90957 | C2 | semidirect |
| 7. #90955 | C2 | semidirect |
| 24. C2×C8×D5 | D3 | semidirect |
| 41. #1202 | C8 | direct (N × H) |
| 42. C3×C5×C8 | D4 | semidirect |
| 52. C8×Dic3 | D5 | semidirect |
| 70. C2×D15 | C2×C8 | semidirect |
| 73. C2×C3×D5 | C2×C8 | semidirect |
| 79. C5×Dic3 | C2×C8 | semidirect |
| 106. C5×C8 | #67 | semidirect |
| 134. C3×C8 | D20 | semidirect |
| 143. C2×D5 | D3×C8 | semidirect |
| 163. C3×C5 | C8×D4 | semidirect |
| 176. Dic3 | C8×D5 | semidirect |
| 197. C8 | #1202 | direct (N × H) |
| 203. C5 | C8×#67 | semidirect |
| 217. C3 | C8×D20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D15 | 2 |
| C2×C3×C8×D5 | 2 |
| C4×#1202 | 2 |
| C5×C8×Dic3 | 2 |
| Dic3⋊#168 | 2 |
| #90957 | 2 |
| #90955 | 2 |
| C8×D20 | 3 |
| C8×#67 | 5 |