Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
216 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×C4×ΓL(1,𝔽16) | C2 | semidirect |
| 3. C3×#6758 | C2 | semidirect |
| 4. #91239 | C3 | direct (N × H) |
| 7. C32×C5×Q8 | C4 | semidirect |
| 9. C32×D20 | C4 | semidirect |
| 17. C4×ΓL(1,𝔽16) | C2×C3 | semidirect |
| 18. #6758 | C2×C3 | semidirect |
| 34. C3×C5×Q8 | Dic3 | semidirect |
| 35. C3×C5×Q8 | C3×C4 | semidirect |
| 40. C3×D20 | Dic3 | semidirect |
| 41. C3×D20 | C3×C4 | semidirect |
| 58. C32×Q8 | AGL(1,𝔽5) | semidirect |
| 89. C32×C5 | #104 | semidirect |
| 91. C5×Q8 | C3×Dic3 | semidirect |
| 93. D20 | C3×Dic3 | semidirect |
| 114. C3×Q8 | C3×AGL(1,𝔽5) | semidirect |
| 115. C3×Q8 | ΓL(1,𝔽16) | semidirect |
| 145. C3×C5 | #837 | semidirect |
| 146. C3×C5 | C3×#104 | semidirect |
| 167. C32 | #4010 | semidirect |
| 168. Q8 | C3×ΓL(1,𝔽16) | semidirect |
| 184. C5 | C3×#837 | semidirect |
| 192. C3 | C3×#4010 | semidirect |
| 193. C3 | #91239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#713 | 2 |
| C3×C4×ΓL(1,𝔽16) | 2 |
| C3×#6758 | 2 |
| #91239 | 3 |
| C3×#4010 | 3 |
| C3×#837 | 5 |