Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
319 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 49 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⋊GU(2,𝔽3))⋊C3 | C2 | semidirect |
| 3. #10593657 | C3 | semidirect |
| 5. #41⋊H(3,𝔽3) | C4 | semidirect |
| 7. C2×Q8⋊H(3,𝔽3) | C4 | semidirect |
| 14. C3⋊GU(2,𝔽3) | C2×C3 | semidirect |
| 32. C3×#41⋊C3 | C3×C4 | semidirect |
| 35. C2×C3×SL(2,𝔽3) | C3×C4 | semidirect |
| 235. C32 | #5423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41⋊H(3,𝔽3) | 2 |
| (C3⋊GU(2,𝔽3))⋊C3 | 2 |
| #10593657 | 3 |
| C3×#5236 | 3 |
| #3748⋊C3 | 4 |