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 |
|---|---|---|
| 1. C2×C3×D60 | C2 | semidirect |
| 2. C2×C5×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. #10623822 | C2 | direct (N × H) |
| 8. C3×D60 | C22 | semidirect |
| 9. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 11. C2×D60 | D3 | semidirect |
| 23. C2×C3⋊(C3⋊C8) | D5 | semidirect |
| 30. D60 | C2×D3 | semidirect |
| 36. C2×C32×C5 | D8 | semidirect |
| 46. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 62. C32×C5 | C2×D8 | semidirect |
| 76. C2×C3×C5 | #213 | semidirect |
| 95. C2×C32 | D40 | semidirect |
| 102. C3×C5 | C2×#213 | semidirect |
| 113. C2×C5 | #3713 | semidirect |
| 116. C32 | C2×D40 | semidirect |
| 125. C2×C3 | #6653 | semidirect |
| 128. C5 | C2×#3713 | semidirect |
| 135. C3 | C2×#6653 | semidirect |
| 137. C2 | #10623822 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D60 | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| #10623822 | 2 |
| C2×#6653 | 3 |
| C2×#3713 | 5 |