Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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×C8×C3⋊D3 | C2 | semidirect |
| 3. C3×C8×D15 | C2 | semidirect |
| 4. #10623818 | C2 | semidirect |
| 5. #10623817 | C2 | semidirect |
| 12. C32×C5×C8 | C22 | semidirect |
| 13. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 14. C3×C3⋊#168 | C22 | semidirect |
| 17. C8×D15 | D3 | semidirect |
| 26. (C3⋊D3)⋊D5 | C8 | direct (N × H) |
| 32. C8×C3⋊D3 | D5 | semidirect |
| 45. C3×C5×C8 | C2×D3 | semidirect |
| 46. C3⋊#168 | C2×D3 | semidirect |
| 52. C5×C3⋊D3 | C2×C8 | semidirect |
| 53. C3×D15 | C2×C8 | semidirect |
| 64. C32×C8 | C2×D5 | semidirect |
| 65. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 86. C32×C5 | C22×C8 | semidirect |
| 93. C5×C8 | D32 | semidirect |
| 104. D15 | D3×C8 | semidirect |
| 118. C3×C8 | D3×D5 | semidirect |
| 129. C3⋊D3 | C8×D5 | semidirect |
| 137. C3×C5 | C2×D3×C8 | semidirect |
| 152. C32 | C2×C8×D5 | semidirect |
| 160. C8 | (C3⋊D3)⋊D5 | direct (N × H) |
| 167. C5 | D32×C8 | semidirect |
| 175. C3 | D3×C8×D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×(C3⋊D3)⋊D5 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×C8×D15 | 2 |
| #10623818 | 2 |
| #10623817 | 2 |
| D3×C8×D5 | 3 |
| D32×C8 | 5 |