Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
254 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 254 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 |
|---|---|---|
| 2. C3×C4⋊ΓL(1,𝔽16) | C2 | semidirect |
| 3. C3×D5⋊(C3⋊C8) | C2 | semidirect |
| 4. #91236 | C3 | direct (N × H) |
| 8. C32×C5×D4 | C4 | semidirect |
| 10. C32×D20 | C4 | semidirect |
| 17. C4⋊ΓL(1,𝔽16) | C2×C3 | semidirect |
| 18. D5⋊(C3⋊C8) | C2×C3 | semidirect |
| 39. C3×C5×D4 | Dic3 | semidirect |
| 40. C3×C5×D4 | C3×C4 | semidirect |
| 45. C3×D20 | Dic3 | semidirect |
| 46. C3×D20 | C3×C4 | semidirect |
| 65. C32×D4 | AGL(1,𝔽5) | semidirect |
| 99. C32×C5 | #102 | semidirect |
| 102. C5×D4 | C3×Dic3 | semidirect |
| 104. D20 | C3×Dic3 | semidirect |
| 141. C3×D4 | C3×AGL(1,𝔽5) | semidirect |
| 142. C3×D4 | ΓL(1,𝔽16) | semidirect |
| 167. C3×C5 | #832 | semidirect |
| 168. C3×C5 | C3×#102 | semidirect |
| 197. C32 | #4007 | semidirect |
| 201. D4 | C3×ΓL(1,𝔽16) | semidirect |
| 220. C5 | C3×#832 | semidirect |
| 230. C3 | C3×#4007 | semidirect |
| 231. C3 | #91236 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D4×D5 | 2 |
| C3×C4⋊ΓL(1,𝔽16) | 2 |
| C3×D5⋊(C3⋊C8) | 2 |
| #91236 | 3 |
| C3×#4007 | 3 |
| C3×#832 | 5 |