Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 7. C2×C3⋊ΓL(1,𝔽16) | C4 | semidirect |
| 8. C2×C32×C4×C5 | C4 | semidirect |
| 9. C2×C32×Dic5 | C4 | semidirect |
| 29. C2×C3×C4×C5 | Dic3 | semidirect |
| 30. C2×C3×Dic5 | Dic3 | semidirect |
| 43. C2×C32×C4 | AGL(1,𝔽5) | semidirect |
| 57. C32×C5 | #95 | semidirect |
| 62. C2×C4×C5 | C3⋊Dic3 | semidirect |
| 63. C2×Dic5 | C3⋊Dic3 | semidirect |
| 82. C2×C3×C4 | ΓL(1,𝔽16) | semidirect |
| 101. C3×C5 | C3⋊#95 | semidirect |
| 115. C32 | (C2×AGL(1,𝔽5))⋊C4 | semidirect |
| 122. C2×C4 | C3⋊ΓL(1,𝔽16) | semidirect |
| 128. C5 | #63658 | semidirect |
| 137. C3 | #91235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊ΓL(1,𝔽16) | 2 |
| C2×C32×C4×D5 | 2 |
| #91235 | 3 |
| #63658 | 5 |