Finite Group DatabasebetaFinite Group Databasebeta← C22⋊C4×((C3⋊D3)⋊C3)⋊C2 #13148705
Order 1728.
2491 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 2491 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
| C2×C4×((C3⋊D3)⋊C3)⋊C2 | 2 |
| C22⋊C4×#272 | 2 |
| C22⋊C4×(C3⋊D3)⋊C3 | 2 |
| #11721320 | 2 |
| #11721310 | 2 |
| #11721161 | 2 |
| #11721160 | 2 |
| D32×C22⋊C4 | 3 |