Finite Group DatabasebetaFinite Group Databasebeta← C2×C4⋊((C3⋊D3)⋊A4) #13164609
Order 1728.
1664 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|
| C22×(C3⋊D3)⋊A4 | 2 |
| C2×C4×C22⋊H(3,𝔽3) | 2 |
| C4⋊((C3⋊D3)⋊A4) | 2 |
| C23×C4⋊(C3⋊D3) | 3 |
| C2×A4×D12 | 3 |
| C2×C4⋊((C3⋊D3)⋊C3) | 4 |