Finite Group DatabasebetaFinite Group DatabasebetaOrder 29988.
230 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 43 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×C17 | C22×C3 |
| LCS | G ▷ C3×C72×C17 | |
| 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 |
|---|---|
| D51×#3861 | 2 |
| C3⋊(C17⋊#64423) | 2 |
| C3×C17×#64423 | 2 |
| C7×D7×D51 | 3 |
| D17×#64423 | 3 |
| C2×ΓL(1,𝔽8)×D51 | 7 |
| AGL(1,𝔽7)×D51 | 7 |
| D3×#64423 | 17 |