Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
254 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×C3×C3⋊#170 | C2 | semidirect |
| 3. #91232 | C3 | direct (N × H) |
| 14. C2×C3⋊#170 | C2×C3 | semidirect |
| 19. C2×C32×D5 | C8 | semidirect |
| 62. C2×C3×D5 | C3⋊C8 | semidirect |
| 63. C2×C3×D5 | C3×C8 | semidirect |
| 75. C32×C5 | C22⋊C8 | semidirect |
| 117. C2×D5 | C3×C3⋊C8 | semidirect |
| 127. C3×C5 | #830 | semidirect |
| 128. C3×C5 | C3×C22⋊C8 | semidirect |
| 151. C32 | #4003 | semidirect |
| 169. C5 | C3×#830 | semidirect |
| 177. C3 | C3×#4003 | semidirect |
| 178. C3 | #91232 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D5 | 2 |
| C2×C3×C3⋊#170 | 2 |
| #91232 | 3 |
| C3×#4003 | 3 |
| C3×#830 | 5 |