Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 288 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×C5×D8 | C2 | semidirect |
| 2. C3×#4086 | C2 | semidirect |
| 3. C3×#4082 | C2 | semidirect |
| 4. C2×C3×#687 | C2 | semidirect |
| 5. C2×C3×#686 | C2 | semidirect |
| 6. C2×C3×#677 | C2 | semidirect |
| 7. C3×#3947 | C2 | semidirect |
| 8. #65443 | C3 | direct (N × H) |
| 23. C2×C5×D8 | C2×C3 | semidirect |
| 24. #4086 | C2×C3 | semidirect |
| 25. #4082 | C2×C3 | semidirect |
| 26. C2×#687 | C2×C3 | semidirect |
| 27. C2×#686 | C2×C3 | semidirect |
| 28. C2×#677 | C2×C3 | semidirect |
| 29. #3947 | C2×C3 | semidirect |
| 45. C3×C5×C8 | D4 | semidirect |
| 46. C3×#168 | D4 | semidirect |
| 50. C2×C3×D8 | D5 | semidirect |
| 107. C5×C8 | C3×D4 | semidirect |
| 108. #168 | C3×D4 | semidirect |
| 112. C2×D8 | C3×D5 | semidirect |
| 137. C3×C8 | C22⋊D5 | semidirect |
| 162. C3×C5 | #496 | semidirect |
| 195. C8 | C3×C22⋊D5 | semidirect |
| 201. C5 | C3×#496 | semidirect |
| 213. C3 | #65443 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D8 | 2 |
| C3×#4086 | 2 |
| C3×#4082 | 2 |
| C2×C3×#687 | 2 |
| C2×C3×#686 | 2 |
| C2×C3×#677 | 2 |
| C3×#3947 | 2 |
| #65443 | 3 |
| C3×#496 | 5 |