Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
126 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 60 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. C3×C5×C3⋊C16 | C2 | semidirect |
| 5. #90934 | C3 | direct (N × H) |
| 14. C3⋊#672 | C2×C3 | semidirect |
| 16. C5×C3⋊C16 | C2×C3 | semidirect |
| 23. C3×C3⋊C16 | D5 | semidirect |
| 58. C3⋊C16 | C3×D5 | semidirect |
| 59. C32×C5 | M32 | semidirect |
| 91. C3×C5 | #812 | semidirect |
| 92. C3×C5 | C3×M32 | semidirect |
| 104. C32 | #3930 | semidirect |
| 114. C5 | C3×#812 | semidirect |
| 119. C3 | #90934 | direct (N × H) |
| 120. C3 | C3×#3930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×D5 | 2 |
| C3×C3⋊#672 | 2 |
| C3×C5×C3⋊C16 | 2 |
| C3×#3930 | 3 |
| #90934 | 3 |
| C3×#812 | 5 |