Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 130 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×#3664 | C2 | semidirect |
| 3. C2×C3×Dic36 | C2 | semidirect |
| 4. C3×#63437 | C2 | semidirect |
| 5. C3×C4×C8×C9 | C2 | semidirect |
| 7. #10588378 | C3 | direct (N × H) |
| 23. C2×#3664 | C2×C3 | semidirect |
| 24. C2×Dic36 | C2×C3 | semidirect |
| 25. #63437 | C2×C3 | semidirect |
| 27. C4×C8×C9 | C2×C3 | semidirect |
| 77. C3×C4×C8 | D9 | semidirect |
| 150. C4×C8 | C3×D9 | semidirect |
| 151. C3×C9 | #495 | semidirect |
| 213. C9 | C3×#495 | semidirect |
| 240. C3 | #10588378 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| C2×C3×#3664 | 2 |
| C2×C3×Dic36 | 2 |
| C3×#63437 | 2 |
| C3×C4×C8×C9 | 2 |
| C3×#4696 | 3 |
| #10588378 | 3 |