Finite Group DatabasebetaFinite Group Databasebeta← D3×C3⋊(C7⋊(C11⋊D11)) #44479220
Order 30492.
616 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 172 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 | C32×C7×C112 | C22 |
| LCS | G ▷ C32×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 |
|---|---|
| C3×D3×C7×C112 | 2 |
| C3×C3⋊(C7⋊(C11⋊D11)) | 2 |
| C3⋊(C3⋊(C7⋊(C11⋊D11))) | 2 |
| C2×C3⋊(C7⋊(C11⋊D11)) | 3 |
| D3×C7⋊(C11⋊D11) | 3 |
| D3×C3⋊(C11⋊D11) | 7 |
| D3×D231 | 11 |