Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
590 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 128 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. C32×#870 | C2 | semidirect |
| 3. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C3×#63565 | C2 | semidirect |
| 8. #10590278 | C3 | direct (N × H) |
| 22. C3×#870 | D3 | semidirect |
| 23. C3×#870 | C2×C3 | semidirect |
| 24. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 32. #63565 | C2×C3 | semidirect |
| 90. #870 | C3×D3 | semidirect |
| 216. C33 | #488 | semidirect |
| 321. C32 | #5056 | semidirect |
| 322. C32 | #5068 | semidirect |
| 323. C32 | C3×#488 | semidirect |
| 361. C3 | #10590278 | direct (N × H) |
| 362. C3 | C3×#5056 | semidirect |
| 363. C3 | C3×#5068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#875 | 2 |
| C32×#870 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C3×#63565 | 2 |
| C3×#63562 | 2 |
| C3×#5068 | 3 |
| C3×#5056 | 3 |
| #10590278 | 3 |