Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 143 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×C32×C5×D4 | C2 | semidirect |
| 2. C2×C4⋊(C3⋊D15) | C2 | semidirect |
| 3. #10623909 | C2 | direct (N × H) |
| 4. C2×C3⋊(C3⋊#168) | C2 | semidirect |
| 9. C32×C5×D4 | C22 | semidirect |
| 12. C4⋊(C3⋊D15) | C22 | semidirect |
| 13. C3⋊(C3⋊#168) | C22 | semidirect |
| 15. C2×C3×C5×D4 | D3 | semidirect |
| 27. C2×C32×D4 | D5 | semidirect |
| 34. C3×C5×D4 | C2×D3 | semidirect |
| 41. C2×C32×C5 | D8 | semidirect |
| 44. C2×C5×D4 | C3⋊D3 | semidirect |
| 51. C32×D4 | C2×D5 | semidirect |
| 63. C2×C3×D4 | D15 | semidirect |
| 67. C32×C5 | C2×D8 | semidirect |
| 71. C5×D4 | C2×C3⋊D3 | semidirect |
| 85. C2×C3×C5 | #213 | semidirect |
| 91. C3×D4 | C2×D15 | semidirect |
| 104. C2×C32 | #686 | semidirect |
| 108. C2×D4 | C3⋊D15 | semidirect |
| 111. C3×C5 | C2×#213 | semidirect |
| 120. C2×C5 | #3753 | semidirect |
| 123. C32 | C2×#686 | semidirect |
| 129. D4 | C2×C3⋊D15 | semidirect |
| 133. C2×C3 | #6715 | semidirect |
| 136. C5 | C2×#3753 | semidirect |
| 144. C3 | C2×#6715 | semidirect |
| 147. C2 | #10623909 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C4⋊(C3⋊D15) | 2 |
| #10623909 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| C2×#6715 | 3 |
| C2×#3753 | 5 |