Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
216 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 39 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×C72×C19 | C22×C3 |
| LCS | G ▷ C3×C72×C19 | |
| 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⋊#19150308 | 2 |
| C3⋊#19150306 | 2 |
| C3×C7×#11716321 | 2 |
| D19×C3⋊(C7⋊D7) | 3 |
| #11716321⋊D7 | 3 |
| D21×D19⋊C3 | 7 |
| #11716321⋊D3 | 7 |
| C2×C3⋊(ΓL(1,𝔽8)⋊D7) | 19 |