Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
166 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 3. #91222 | C3 | direct (N × H) |
| 7. C32×C5×C8 | C4 | semidirect |
| 8. C32×#168 | C4 | semidirect |
| 28. C3×C5×C8 | Dic3 | semidirect |
| 29. C3×C5×C8 | C3×C4 | semidirect |
| 31. C3×#168 | Dic3 | semidirect |
| 32. C3×#168 | C3×C4 | semidirect |
| 42. C32×C8 | AGL(1,𝔽5) | semidirect |
| 59. C32×C5 | #106 | semidirect |
| 62. C5×C8 | C3×Dic3 | semidirect |
| 63. #168 | C3×Dic3 | semidirect |
| 84. C3×C8 | C3×AGL(1,𝔽5) | semidirect |
| 85. C3×C8 | ΓL(1,𝔽16) | semidirect |
| 95. C3×C5 | #817 | semidirect |
| 96. C3×C5 | C3×#106 | semidirect |
| 110. C32 | #3993 | semidirect |
| 114. C8 | C3×ΓL(1,𝔽16) | semidirect |
| 121. C5 | C3×#817 | semidirect |
| 127. C3 | C3×#3993 | semidirect |
| 128. C3 | #91222 | 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 |
| C32×C8×D5 | 2 |
| #91222 | 3 |
| C3×#3993 | 3 |
| C3×#817 | 5 |