Finite Group DatabasebetaFinite Group Databasebeta← C22×C4×((C3⋊D3)⋊C3)⋊C2 #13164718
Order 1728.
5003 conjugacy classes of subgroups; only the 971 normal subgroups are shown.
This group has 5003 conjugacy classes of subgroups — too many to draw. Only its 971 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 |
|---|---|
| C23×((C3⋊D3)⋊C3)⋊C2 | 2 |
| C22×C4×#272 | 2 |
| C22×C4×(C3⋊D3)⋊C3 | 2 |
| C22×#6199 | 2 |
| C22×((C3⋊D3)⋊C3)⋊C4 | 2 |
| C2×C4×((C3⋊D3)⋊C3)⋊C2 | 2 |
| C22×C4×D32 | 3 |