Finite Group DatabasebetaFinite Group Databasebeta← C23×C4⋊((C3⋊D3)⋊C3) #13164901
Order 1728.
5003 conjugacy classes of subgroups; only the 1204 normal subgroups are shown.
This group has 5003 conjugacy classes of subgroups — too many to draw. Only its 1204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
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 |
|---|---|
| C24×(C3⋊D3)⋊C3 | 2 |
| C23×C4×H(3,𝔽3) | 2 |
| C22×C4⋊((C3⋊D3)⋊C3) | 2 |
| C23×C4⋊(C3⋊D3) | 3 |
| C23×C3×D12 | 3 |