Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
197 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 4. #10589356 | C3 | semidirect |
| 9. (C3⋊(C3⋊C16))⋊C3 | C4 | semidirect |
| 33. C3⋊(C3⋊C16) | C3×C4 | semidirect |
| 99. H(3,𝔽3) | #367 | semidirect |
| 152. C32 | #4490 | semidirect |
| 153. C32 | C3×#367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#107 | 2 |
| #63645⋊C3 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #10589356 | 3 |
| C3×#4490 | 3 |