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. #91223 | 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 |
| 43. C32×C8 | AGL(1,𝔽5) | semidirect |
| 60. C32×C5 | #107 | semidirect |
| 63. C5×C8 | C3×Dic3 | semidirect |
| 64. #168 | C3×Dic3 | semidirect |
| 88. C3×C8 | C3×AGL(1,𝔽5) | semidirect |
| 89. C3×C8 | ΓL(1,𝔽16) | semidirect |
| 100. C3×C5 | #818 | semidirect |
| 101. C3×C5 | C3×#107 | semidirect |
| 116. C32 | #3994 | semidirect |
| 120. C8 | C3×ΓL(1,𝔽16) | semidirect |
| 130. C5 | C3×#818 | semidirect |
| 136. C3 | C3×#3994 | semidirect |
| 137. C3 | #91223 | 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 |
| #91223 | 3 |
| C3×#3994 | 3 |
| C3×#818 | 5 |