Finite Group DatabasebetaFinite Group Databasebeta← AGL(1,𝔽5)×ΓL(1,𝔽8)×GL(2,𝔽3) #72218820
Order 20160.
748 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|
| C4×ΓL(1,𝔽8)×GL(2,𝔽3) | 5 |
| C7×AGL(1,𝔽5)×GL(2,𝔽3) | 3 |
| ΓL(1,𝔽8)×#91886 | 2 |
| D5×ΓL(1,𝔽8)×GL(2,𝔽3) | 2 |
| SD16×AGL(1,𝔽5)×ΓL(1,𝔽8) | 3 |
| AGL(1,𝔽5)×ΓL(1,𝔽8)×SL(2,𝔽3) | 2 |
| C3×AGL(1,𝔽5)×GL(2,𝔽3) | 7 |
| C2×D3×AGL(1,𝔽5)×ΓL(1,𝔽8) | 4 |