Finite Group DatabasebetaFinite Group Databasebeta← D7×AGL(1,𝔽5)×SL(2,𝔽3) #72218646
Order 6720.
432 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|
| Q8×D7×AGL(1,𝔽5) | 3 |
| SL(2,𝔽3)×C7⋊AGL(1,𝔽5) | 2 |
| C7×AGL(1,𝔽5)×SL(2,𝔽3) | 2 |
| D5×D7×SL(2,𝔽3) | 2 |
| C2×C3×D7×AGL(1,𝔽5) | 4 |
| C4×D7×SL(2,𝔽3) | 5 |
| C2×AGL(1,𝔽5)×SL(2,𝔽3) | 7 |