Finite Group DatabasebetaFinite Group Databasebeta← (C3⋊AGL(1,𝔽7))⋊(C11⋊D11) #44479111
Order 30492.
616 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 121 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 | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C112 | C22×C3 |
| LCS | G ▷ C3×C7×C112 | |
| UCS | C1 | |
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 |
|---|---|
| ΓL(1,𝔽8)×C3⋊(C11⋊D11) | 2 |
| C112×C3⋊AGL(1,𝔽7) | 2 |
| C3×C11⋊(C11⋊AGL(1,𝔽7)) | 2 |
| D21⋊(C11⋊D11) | 3 |
| AGL(1,𝔽7)×C11⋊D11 | 3 |
| C3×D3×C11⋊D11 | 7 |
| D33⋊AGL(1,𝔽7) | 11 |