Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 158 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×#6710 | C2 | semidirect |
| 3. C2×C3×C3⋊#168 | C2 | semidirect |
| 4. #91837 | C3 | direct (N × H) |
| 15. #6710 | C2×C3 | semidirect |
| 16. C2×C3⋊#168 | C2×C3 | semidirect |
| 67. C32×C5 | #131 | semidirect |
| 105. C3×C5 | #948 | semidirect |
| 106. C3×C5 | C3×#131 | semidirect |
| 118. C32 | #4094 | semidirect |
| 130. C5 | C3×#948 | semidirect |
| 135. C3 | C3×#4094 | semidirect |
| 136. C3 | #91837 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| C3×#6710 | 2 |
| C2×C3×C3⋊#168 | 2 |
| #91837 | 3 |
| C3×#4094 | 3 |
| C3×#948 | 5 |