Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
198 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 198 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 |
|---|---|---|
| 4. C8×ΓL(1,𝔽16) | C3 | direct (N × H) |
| 8. C3×C3⋊#170 | C4 | semidirect |
| 9. C32×C5×C8 | C4 | semidirect |
| 10. C32×#168 | C4 | semidirect |
| 20. C3×ΓL(1,𝔽16) | C8 | direct (N × H) |
| 32. C3⋊#170 | C3×C4 | semidirect |
| 35. C3×C5×C8 | Dic3 | semidirect |
| 36. C3×C5×C8 | C3×C4 | semidirect |
| 38. C3×#168 | Dic3 | semidirect |
| 39. C3×#168 | C3×C4 | semidirect |
| 50. C32×C8 | AGL(1,𝔽5) | semidirect |
| 55. ΓL(1,𝔽16) | C3×C8 | direct (N × H) |
| 70. C32×C5 | C4×C8 | semidirect |
| 74. C5×C8 | C3×Dic3 | semidirect |
| 75. #168 | C3×Dic3 | semidirect |
| 97. C3×C8 | C3×AGL(1,𝔽5) | semidirect |
| 98. C3×C8 | ΓL(1,𝔽16) | direct (N × H) |
| 110. C3×C5 | C8×Dic3 | semidirect |
| 111. C3×C5 | C3×C4×C8 | semidirect |
| 125. C32 | C8×AGL(1,𝔽5) | semidirect |
| 130. C8 | C3×ΓL(1,𝔽16) | direct (N × H) |
| 137. C5 | C3×C8×Dic3 | semidirect |
| 143. C3 | C3×C8×AGL(1,𝔽5) | semidirect |
| 144. C3 | C8×ΓL(1,𝔽16) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×ΓL(1,𝔽16) | 2 |
| C3×D5⋊(C3⋊C8) | 2 |
| C32×C8×D5 | 2 |
| C8×ΓL(1,𝔽16) | 3 |
| C3×C8×AGL(1,𝔽5) | 3 |
| C3×C8×Dic3 | 5 |