Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1231 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1231 conjugacy classes of subgroups — too many to draw. Only its 288 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. H(3,𝔽3)×#95 | C2 | semidirect |
| 3. #63658⋊C3 | C2 | semidirect |
| 4. C3⋊D3×#95 | C3 | semidirect |
| 10. C2×C4×(C3⋊D3)⋊C3 | C4 | semidirect |
| 14. C32×#95 | D3 | semidirect |
| 15. C32×#95 | C2×C3 | semidirect |
| 16. #63658 | C2×C3 | semidirect |
| 23. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 25. C2×(C3⋊Dic3)⋊C3 | C2×C4 | semidirect |
| 37. C2×C4×C3⋊D3 | C3×C4 | semidirect |
| 72. C2×C32×C4 | C4×D3 | semidirect |
| 73. C2×C32×C4 | C2×C3×C4 | semidirect |
| 75. C2×C3⋊Dic3 | C2×C3×C4 | semidirect |
| 84. (C3⋊D3)⋊C3 | #95 | direct (N × H) |
| 123. #95 | (C3⋊D3)⋊C3 | direct (N × H) |
| 124. H(3,𝔽3) | C2×#95 | semidirect |
| 164. C3⋊D3 | C3×#95 | semidirect |
| 200. C32 | D3×#95 | semidirect |
| 201. C32 | C2×C3×#95 | semidirect |
| 210. C2×C4 | C4×(C3⋊D3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×(C3⋊D3)⋊C3 | 2 |
| H(3,𝔽3)×#95 | 2 |
| #63658⋊C3 | 2 |
| C3⋊D3×#95 | 3 |
| C3×D3×#95 | 3 |