Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11716328⋊D7 |
| commutator, cosocle, hypocenter | C72×C19 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
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×#19150318 | 2 |
| C3×#19150309 | 2 |
| C3×C7×#11716328 | 2 |
| C3×(C7⋊D7)⋊D19 | 3 |
| #11716328⋊D7 | 3 |
| C3×D7×D19⋊C3 | 7 |
| C3×#11716322⋊C2 | 7 |
| C3×D7×AGL(1,𝔽7) | 19 |