Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
534 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 138 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. C2×C3×#3672 | C2 | semidirect |
| 3. C3×#63431 | C2 | semidirect |
| 4. C3×C4×C9⋊C8 | C2 | semidirect |
| 6. #10588753 | C3 | direct (N × H) |
| 20. C2×#3672 | C2×C3 | semidirect |
| 21. #63431 | C2×C3 | semidirect |
| 22. C4×C9⋊C8 | C2×C3 | semidirect |
| 30. C3×C9⋊C8 | D4 | semidirect |
| 53. C3×C4×C9 | SD16 | semidirect |
| 85. C9⋊C8 | C3×D4 | semidirect |
| 121. C4×C9 | C3×SD16 | semidirect |
| 128. C3×C9 | #492 | semidirect |
| 178. C3×C4 | #3672 | semidirect |
| 185. C9 | C3×#492 | semidirect |
| 207. C4 | C3×#3672 | semidirect |
| 210. C3 | #10588753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#127 | 2 |
| C2×C3×#3672 | 2 |
| C3×#63431 | 2 |
| C3×C4×C9⋊C8 | 2 |
| C3×#5076 | 3 |
| #10588753 | 3 |