Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 120 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×C5×C3⋊C8 | C2 | semidirect |
| 4. C3×#6649 | C2 | semidirect |
| 5. C3×D5×C3⋊C8 | C2 | semidirect |
| 7. #91283 | C3 | direct (N × H) |
| 21. #6710 | C2×C3 | semidirect |
| 22. C2×C5×C3⋊C8 | C2×C3 | semidirect |
| 26. #6649 | C2×C3 | semidirect |
| 27. D5×C3⋊C8 | C2×C3 | semidirect |
| 38. C2×C3×C3⋊C8 | D5 | semidirect |
| 103. C2×C3⋊C8 | C3×D5 | semidirect |
| 104. C32×C5 | #131 | semidirect |
| 163. C3×C5 | #948 | semidirect |
| 164. C3×C5 | C3×#131 | semidirect |
| 183. C32 | #4047 | semidirect |
| 201. C5 | C3×#948 | semidirect |
| 208. C3 | #91283 | direct (N × H) |
| 209. C3 | C3×#4047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#709 | 2 |
| C3×#6710 | 2 |
| C2×C3×C5×C3⋊C8 | 2 |
| C3×#6649 | 2 |
| C3×D5×C3⋊C8 | 2 |
| C3×#4047 | 3 |
| #91283 | 3 |
| C3×#948 | 5 |