Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3107 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 3107 conjugacy classes of subgroups — too many to draw. Only its 459 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. C23×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 3. C2×#88451 | C2 | direct (N × H) |
| 7. C23×#272 | C4 | semidirect |
| 10. C22×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 11. #88451 | C22 | direct (N × H) |
| 14. C23×C3⋊Dic3 | D3 | semidirect |
| 22. C22×#272 | C2×C4 | semidirect |
| 25. C2×(C3⋊Dic3)⋊C3 | C23 | semidirect |
| 38. C22×C3⋊Dic3 | C2×D3 | semidirect |
| 42. C22×H(3,𝔽3) | C22⋊C4 | semidirect |
| 48. C2×#272 | C22×C4 | semidirect |
| 75. C2×C3⋊Dic3 | C22×D3 | semidirect |
| 79. C2×H(3,𝔽3) | C2×C22⋊C4 | semidirect |
| 108. C22×C32 | (C2×D3)⋊C4 | semidirect |
| 125. H(3,𝔽3) | C22×C22⋊C4 | semidirect |
| 158. C2×C32 | C2×(C2×D3)⋊C4 | semidirect |
| 198. C32 | C22×(C2×D3)⋊C4 | semidirect |
| 224. C22 | #88451 | direct (N × H) |
| 233. C2 | C2×#88451 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#272 | 2 |
| C23×(C3⋊Dic3)⋊C3 | 2 |
| C2×#88451 | 2 |
| C22×(C2×D3)⋊Dic3 | 3 |