Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
684 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 144 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×#3667⋊C3 | C2 | semidirect |
| 4. #63391⋊C3 | C3 | direct (N × H) |
| 5. C3×#63391 | C3 | semidirect |
| 16. #3667⋊C3 | C2×C3 | semidirect |
| 17. C3×#3667 | C2×C3 | semidirect |
| 25. #63391 | C32 | semidirect |
| 57. #3667 | C2×C32 | semidirect |
| 81. C3×3−1+2 | #100 | semidirect |
| 160. 3−1+2 | C3×#100 | semidirect |
| 162. C3×C9 | C3×#100 | semidirect |
| 223. C9 | C32×#100 | semidirect |
| 246. C3 | #63391⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×3−1+2 | 2 |
| C3×#3667⋊C3 | 2 |
| C32×#833 | 3 |
| #63391⋊C3 | 3 |
| C3×#63391 | 3 |