Finite Group DatabasebetaFinite Group Databasebeta← C2×AGL(1,𝔽7)×PSU(3,𝔽2) #72230661
Order 6048.
708 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 187 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×ΓL(1,𝔽8)⋊PSU(3,𝔽2) | 2 |
| C2×D7×PSU(3,𝔽2) | 3 |
| C2×ΓL(1,𝔽8)×PSU(3,𝔽2) | 2 |
| AGL(1,𝔽7)×PSU(3,𝔽2) | 2 |
| C2×#157×AGL(1,𝔽7) | 2 |
| C22×C3×PSU(3,𝔽2) | 7 |
| C2×Q8×AGL(1,𝔽7) | 9 |