Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10623983 | C2 | direct (N × H) |
| 10. C3×C3⋊#170 | C22 | semidirect |
| 14. C2×C3⋊#170 | D3 | semidirect |
| 37. C3⋊#170 | C2×D3 | semidirect |
| 40. C2×C32×C5 | M16 | semidirect |
| 69. C32×C5 | C2×M16 | semidirect |
| 85. C2×C3×C5 | ΓL(1,𝔽25) | semidirect |
| 107. C2×C32 | #700 | semidirect |
| 114. C3×C5 | C2×ΓL(1,𝔽25) | semidirect |
| 127. C2×C5 | #3712 | semidirect |
| 130. C32 | C2×#700 | semidirect |
| 139. C2×C3 | #6740 | semidirect |
| 143. C5 | C2×#3712 | semidirect |
| 151. C3 | C2×#6740 | semidirect |
| 153. C2 | #10623983 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67137 | 2 |
| C2×C3×C3⋊#170 | 2 |
| #10623983 | 2 |
| C2×#6740 | 3 |
| C2×#3712 | 5 |