Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1606 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 1606 conjugacy classes of subgroups — too many to draw. Only its 247 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.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊(C3⋊#226) | C2 | direct (N × H) |
| 7. C3⋊(C3⋊#226) | C22 | direct (N × H) |
| 72. C22×C32 | #226 | semidirect |
| 99. C2×C32 | C2×#226 | semidirect |
| 112. C22×C3 | C3⋊#226 | semidirect |
| 119. C32 | C22×#226 | semidirect |
| 132. C2×C3 | C2×C3⋊#226 | semidirect |
| 134. C22 | C3⋊(C3⋊#226) | direct (N × H) |
| 140. C3 | C22×C3⋊#226 | semidirect |
| 141. C2 | C2×C3⋊(C3⋊#226) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×SL(2,𝔽3) | 2 |
| C2×C3⋊(C3⋊#226) | 2 |
| C22×C3⋊#226 | 3 |
| C22×#3756 | 3 |
| C22×C3⋊(C3⋊Dic3) | 4 |