Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
332 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 106 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×#63432 | C2 | semidirect |
| 3. C3×C4×C8×C9 | C2 | semidirect |
| 5. C3×#63376 | C2 | semidirect |
| 7. #10588379 | C3 | direct (N × H) |
| 21. #63432 | C2×C3 | semidirect |
| 23. C4×C8×C9 | C2×C3 | semidirect |
| 25. #63376 | C2×C3 | semidirect |
| 66. C3×C4×C8 | D9 | semidirect |
| 130. C4×C8 | C3×D9 | semidirect |
| 131. C3×C9 | #488 | semidirect |
| 185. C9 | C3×#488 | semidirect |
| 210. C3 | #10588379 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63437 | 2 |
| C3×#63432 | 2 |
| C3×C4×C8×C9 | 2 |
| C3×#63380 | 2 |
| C3×#63376 | 2 |
| C3×#4697 | 3 |
| #10588379 | 3 |