Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
884 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 238 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×#64078 | C2 | semidirect |
| 3. C33×C4×C8 | C2 | semidirect |
| 4. C3×#63648 | C2 | semidirect |
| 5. #10592393 | C3 | direct (N × H) |
| 16. #64078 | C2×C3 | semidirect |
| 20. C32×C4×C8 | D3 | semidirect |
| 21. C32×C4×C8 | C2×C3 | semidirect |
| 22. #63648 | C2×C3 | semidirect |
| 68. C3×C4×C8 | C3×D3 | semidirect |
| 69. C3×C4×C8 | C3⋊D3 | semidirect |
| 141. C4×C8 | C3×C3⋊D3 | semidirect |
| 142. C33 | #486 | semidirect |
| 207. C32 | #4694 | semidirect |
| 208. C32 | C3×#486 | semidirect |
| 239. C3 | C3×#4694 | semidirect |
| 240. C3 | #10592393 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64083 | 2 |
| C3×#64078 | 2 |
| C33×C4×C8 | 2 |
| C3×#63648 | 2 |
| #10592393 | 3 |
| C3×#4694 | 3 |