Finite Group DatabasebetaFinite Group Databasebeta← AGL(1,𝔽7)×C3⋊GL(2,𝔽3) #72246280
Order 6048.
696 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽7)×C3⋊S4 |
| commutator, cosocle, hypocenter | C3×C7×SL(2,𝔽3) | C22×C3 |
| Fitting | C3×C7×Q8 | C2×C3×D3 |
| socle | C2×C3×C7 | C2×C3×S4 |
| LCS | G ▷ C3×C7×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
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 |
|---|---|
| D7×C3⋊GL(2,𝔽3) | 3 |
| #72246259 | 2 |
| ΓL(1,𝔽8)×C3⋊GL(2,𝔽3) | 2 |
| AGL(1,𝔽7)×#215 | 3 |
| C3×SL(2,𝔽3)×AGL(1,𝔽7) | 2 |
| AGL(1,𝔽7)×GL(2,𝔽3) | 3 |
| C2×C3⋊D3×AGL(1,𝔽7) | 4 |
| C2×C3×C3⋊GL(2,𝔽3) | 7 |