Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 128 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×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×C32×D20 | C2 | semidirect |
| 3. C2×C3⋊(C3⋊#168) | C2 | semidirect |
| 4. #10623757 | C2 | direct (N × H) |
| 10. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 12. C32×D20 | C22 | semidirect |
| 13. C3⋊(C3⋊#168) | C22 | semidirect |
| 16. C2×C3×D20 | D3 | semidirect |
| 28. C2×C4⋊(C3⋊D3) | D5 | semidirect |
| 37. C3×D20 | C2×D3 | semidirect |
| 40. C2×C32×C5 | D8 | semidirect |
| 45. C2×D20 | C3⋊D3 | semidirect |
| 54. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 67. C32×C5 | C2×D8 | semidirect |
| 74. D20 | C2×C3⋊D3 | semidirect |
| 84. C2×C3×C5 | #213 | semidirect |
| 104. C2×C32 | #686 | semidirect |
| 111. C3×C5 | C2×#213 | semidirect |
| 120. C2×C5 | #3753 | semidirect |
| 123. C32 | C2×#686 | semidirect |
| 133. C2×C3 | #6652 | semidirect |
| 136. C5 | C2×#3753 | semidirect |
| 144. C3 | C2×#6652 | semidirect |
| 147. C2 | #10623757 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C32×D20 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| #10623757 | 2 |
| C2×#6652 | 3 |
| C2×#3753 | 5 |