Finite Group DatabasebetaFinite Group DatabasebetaOrder 2880.
1548 conjugacy classes of subgroups; only the 489 normal subgroups are shown.
This group has 1548 conjugacy classes of subgroups — too many to draw. Only its 489 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 |
|---|---|---|
| 6. C4×C3⋊ΓL(1,𝔽16) | C4 | direct (N × H) |
| 7. C32×C42×C5 | C4 | semidirect |
| 8. C32×C4×Dic5 | C4 | semidirect |
| 23. C3×C42×C5 | Dic3 | semidirect |
| 24. C3×C4×Dic5 | Dic3 | semidirect |
| 28. C3⋊ΓL(1,𝔽16) | C42 | direct (N × H) |
| 29. C32×C4×C5 | C42 | semidirect |
| 30. C32×Dic5 | C42 | semidirect |
| 36. C32×C42 | AGL(1,𝔽5) | semidirect |
| 50. C42×C5 | C3⋊Dic3 | semidirect |
| 51. C4×Dic5 | C3⋊Dic3 | semidirect |
| 61. C3×C4×C5 | C4×Dic3 | semidirect |
| 62. C3×Dic5 | C4×Dic3 | semidirect |
| 66. C3×C42 | ΓL(1,𝔽16) | semidirect |
| 68. C32×C5 | C43 | semidirect |
| 77. C32×C4 | C4×AGL(1,𝔽5) | semidirect |
| 91. C4×C5 | C4×C3⋊Dic3 | semidirect |
| 92. Dic5 | C4×C3⋊Dic3 | semidirect |
| 99. C42 | C3⋊ΓL(1,𝔽16) | direct (N × H) |
| 100. C3×C5 | C42×Dic3 | semidirect |
| 104. C3×C4 | C4×ΓL(1,𝔽16) | semidirect |
| 108. C32 | C42×AGL(1,𝔽5) | semidirect |
| 116. C5 | C42×C3⋊Dic3 | semidirect |
| 121. C4 | C4×C3⋊ΓL(1,𝔽16) | direct (N × H) |
| 122. C3 | C42×ΓL(1,𝔽16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊ΓL(1,𝔽16) | 2 |
| C32×C42×D5 | 2 |
| C42×ΓL(1,𝔽16) | 3 |
| C42×C3⋊Dic3 | 5 |