Finite Group DatabasebetaFinite Group DatabasebetaOrder 3528.
474 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #64423 |
| commutator, cosocle, hypocenter | C72 | C23×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C72 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22×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 |
|---|---|
| C22×C3×#3861 | 2 |
| C2×C3×#64423 | 2 |
| C22×C3×C7×D7 | 3 |
| C22×#64423 | 3 |
| C23×C3×ΓL(1,𝔽8) | 7 |
| C22×C3×AGL(1,𝔽7) | 7 |