Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
122 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 68 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. C3×C3⋊#672 | C2 | semidirect |
| 3. C32×#672 | C2 | semidirect |
| 5. D3×#672 | C3 | direct (N × H) |
| 12. C3⋊#672 | C2×C3 | semidirect |
| 15. C3×#672 | D3 | direct (N × H) |
| 16. C3×#672 | C2×C3 | semidirect |
| 34. C3×C5×D3 | C16 | semidirect |
| 37. #672 | C3×D3 | direct (N × H) |
| 55. C32×C5 | C2×C16 | semidirect |
| 67. C5×D3 | C3×C16 | semidirect |
| 79. C3×D3 | #672 | direct (N × H) |
| 84. C3×C5 | D3×C16 | semidirect |
| 85. C3×C5 | C2×C3×C16 | semidirect |
| 95. C32 | C2×#672 | semidirect |
| 103. D3 | C3×#672 | direct (N × H) |
| 104. C5 | C3×D3×C16 | semidirect |
| 109. C3 | D3×#672 | direct (N × H) |
| 110. C3 | C2×C3×#672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D3×C8 | 2 |
| C3×C3⋊#672 | 2 |
| C32×#672 | 2 |
| C2×C3×#672 | 3 |
| D3×#672 | 3 |
| C3×D3×C16 | 5 |