Finite Group DatabasebetaFinite Group Databasebeta← C2×H(3,𝔽3)×(C3⋊D3)⋊C3 #72228893
Order 2916.
1767 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 1767 conjugacy classes of subgroups — too many to draw. Only its 238 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 |
|---|---|
| H(3,𝔽3)×(C3⋊D3)⋊C3 | 2 |
| C2×H(3,𝔽3)2 | 2 |
| C2×C3⋊D3×H(3,𝔽3) | 3 |
| C2×C3×D3×H(3,𝔽3) | 3 |
| C2×C32×(C3⋊D3)⋊C3 | 3 |
| C2×(C3⋊D3)⋊H(3,𝔽3) | 3 |