Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 408 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×#67180 | C2 | semidirect |
| 3. C2×C32×#168 | C2 | semidirect |
| 4. #10623764 | C2 | direct (N × H) |
| 10. #67180 | C22 | semidirect |
| 13. C32×#168 | C22 | semidirect |
| 17. C2×C3×#168 | D3 | semidirect |
| 37. C3×#168 | C2×D3 | semidirect |
| 39. C2×C32×C5 | SD16 | semidirect |
| 45. C2×#168 | C3⋊D3 | semidirect |
| 64. C32×C5 | C2×SD16 | semidirect |
| 72. #168 | C2×C3⋊D3 | semidirect |
| 80. C2×C3×C5 | #204 | semidirect |
| 97. C2×C32 | #687 | semidirect |
| 104. C3×C5 | C2×#204 | semidirect |
| 112. C2×C5 | #3744 | semidirect |
| 114. C32 | C2×#687 | semidirect |
| 123. C2×C3 | #6659 | semidirect |
| 126. C5 | C2×#3744 | semidirect |
| 133. C3 | C2×#6659 | semidirect |
| 135. C2 | #10623764 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C32×#168 | 2 |
| #10623764 | 2 |
| C2×#6659 | 3 |
| C2×#3744 | 5 |