Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1140 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 1140 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. C3×#63659 | C2 | semidirect |
| 4. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #10592769 | C3 | direct (N × H) |
| 18. #64078 | C2×C3 | semidirect |
| 20. #63659 | C2×C3 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 152. C33 | #486 | semidirect |
| 224. C32 | #5070 | semidirect |
| 225. C32 | C3×#486 | semidirect |
| 257. C3 | C3×#5070 | semidirect |
| 258. C3 | #10592769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#127 | 2 |
| C3×#64078 | 2 |
| C3×#63659 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #10592769 | 3 |
| C3×#5070 | 3 |