Finite Group DatabasebetaFinite Group Databasebeta← D3×C19×ΓL(1,𝔽8)⋊D7 #45692306
Order 33516.
216 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D3×ΓL(1,𝔽8)⋊D7 |
| commutator, cosocle, hypocenter | C3×C72 | C22×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C22×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C19 | |
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 |
|---|---|
| C19×C3⋊(ΓL(1,𝔽8)⋊D7) | 2 |
| D3×C7×C19×ΓL(1,𝔽8) | 2 |
| C3×C19×ΓL(1,𝔽8)⋊D7 | 2 |
| D3×C19×C7⋊D7 | 3 |
| C2×C19×ΓL(1,𝔽8)⋊D7 | 3 |
| C3×D3×D7×C19 | 7 |
| D3×C19×AGL(1,𝔽7) | 7 |
| D3×ΓL(1,𝔽8)⋊D7 | 19 |