Finite Group DatabasebetaFinite Group Databasebeta← C2×AGL(1,𝔽5)×AGL(2,𝔽3) #72217986
Order 17280.
2112 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 2112 conjugacy classes of subgroups — too many to draw. Only its 84 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.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,𝔽5)×((C3⋊D3)⋊C3)⋊C2 | 4 |
| C2×C4×AGL(2,𝔽3) | 5 |
| C2×AGL(1,𝔽5)×AΓL(1,𝔽9) | 3 |
| C2×#72213713 | 2 |
| C2×D5×AGL(2,𝔽3) | 2 |
| C2×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3 | 2 |
| AGL(1,𝔽5)×AGL(2,𝔽3) | 2 |
| C2×AGL(1,𝔽5)×GL(2,𝔽3) | 9 |