Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
401 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 3. H(3,𝔽3)×#108 | C2 | semidirect |
| 4. #63649⋊C3 | C2 | semidirect |
| 5. #63646⋊C3 | C2 | semidirect |
| 6. C3⋊D3×#108 | C3 | semidirect |
| 22. C32×#108 | D3 | semidirect |
| 23. C32×#108 | C2×C3 | semidirect |
| 24. #63649 | C2×C3 | semidirect |
| 25. #63646 | C2×C3 | semidirect |
| 115. (C3⋊D3)⋊C3 | #108 | direct (N × H) |
| 168. #108 | (C3⋊D3)⋊C3 | direct (N × H) |
| 169. H(3,𝔽3) | C2×#108 | semidirect |
| 213. C3⋊D3 | C3×#108 | semidirect |
| 253. C32 | D3×#108 | semidirect |
| 254. C32 | C2×C3×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×(C3⋊D3)⋊C3 | 2 |
| C2×C8×(C3⋊D3)⋊C3 | 2 |
| H(3,𝔽3)×#108 | 2 |
| #63649⋊C3 | 2 |
| #63646⋊C3 | 2 |
| C3⋊D3×#108 | 3 |
| C3×D3×#108 | 3 |