Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1343 conjugacy classes of subgroups; only the 252 normal subgroups are shown.
This group has 1343 conjugacy classes of subgroups — too many to draw. Only its 252 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×#638⋊C3 | 2 |
| C2×C22⋊C4×H(3,𝔽3) | 2 |
| #64139⋊C3 | 2 |
| #64095⋊C3 | 2 |
| #64091⋊C3 | 2 |
| #10595964 | 3 |
| C3×#5493 | 3 |