Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
527 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 527 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×C3⋊GU(2,𝔽3) | C2 | direct (N × H) |
| 3. C2×C3⋊GU(2,𝔽3) | C3 | direct (N × H) |
| 6. C32×#41⋊C3 | C4 | semidirect |
| 8. C2×C32×SL(2,𝔽3) | C4 | semidirect |
| 17. C3⋊GU(2,𝔽3) | C2×C3 | direct (N × H) |
| 22. C32×SL(2,𝔽3) | C2×C4 | semidirect |
| 39. C3×#41⋊C3 | Dic3 | semidirect |
| 40. C3×#41⋊C3 | C3×C4 | semidirect |
| 45. C2×C3×SL(2,𝔽3) | Dic3 | semidirect |
| 46. C2×C3×SL(2,𝔽3) | C3×C4 | semidirect |
| 91. C3×SL(2,𝔽3) | C2×Dic3 | semidirect |
| 92. C3×SL(2,𝔽3) | C2×C3×C4 | semidirect |
| 124. #41⋊C3 | C3×Dic3 | semidirect |
| 127. C2×SL(2,𝔽3) | C3×Dic3 | semidirect |
| 209. SL(2,𝔽3) | C2×C3×Dic3 | semidirect |
| 223. C2×C32 | GU(2,𝔽3) | semidirect |
| 274. C32 | C2×GU(2,𝔽3) | semidirect |
| 302. C2×C3 | C3×GU(2,𝔽3) | semidirect |
| 303. C2×C3 | C3⋊GU(2,𝔽3) | direct (N × H) |
| 318. C3 | C2×C3×GU(2,𝔽3) | semidirect |
| 319. C3 | C2×C3⋊GU(2,𝔽3) | direct (N × H) |
| 322. C2 | C3×C3⋊GU(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#41⋊C3 | 2 |
| C3×C3⋊GU(2,𝔽3) | 2 |
| C2×C3⋊GU(2,𝔽3) | 3 |
| C2×C3×GU(2,𝔽3) | 3 |
| C2×C3×#837 | 3 |
| C2×C3×C3⋊(C3⋊C8) | 4 |