Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
604 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 131 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. D3×#3667 | C2 | semidirect |
| 3. #11720575 | C2 | semidirect |
| 4. C3×#63391 | C2 | semidirect |
| 5. #11720296 | C2 | semidirect |
| 15. #88532 | C22 | semidirect |
| 16. C3×#3667 | C22 | semidirect |
| 29. #63391 | D3 | direct (N × H) |
| 69. #3667 | C2×D3 | semidirect |
| 134. D3×C9 | #100 | semidirect |
| 192. C3×C9 | C2×#100 | semidirect |
| 283. C9 | D3×#100 | semidirect |
| 313. D3 | #63391 | direct (N × H) |
| 327. C3 | C2×#63391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D4×C9 | 2 |
| D3×#3667 | 2 |
| #11720575 | 2 |
| C3×#63391 | 2 |
| #11720296 | 2 |
| D3×#833 | 3 |
| C2×#63391 | 3 |