Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
126 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 58 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⋊#674 | C2 | semidirect |
| 3. #91219 | C3 | direct (N × H) |
| 12. C3⋊#674 | C2×C3 | semidirect |
| 52. C32×C5 | M32 | semidirect |
| 83. C3×C5 | #812 | semidirect |
| 84. C3×C5 | C3×M32 | semidirect |
| 96. C32 | #3990 | semidirect |
| 106. C5 | C3×#812 | semidirect |
| 111. C3 | C3×#3990 | semidirect |
| 112. C3 | #91219 | direct (N × H) |
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⋊#674 | 2 |
| #91219 | 3 |
| C3×#3990 | 3 |
| C3×#812 | 5 |