Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
674 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 674 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×#63630 | C2 | semidirect |
| 4. C3×#63562 | C2 | semidirect |
| 7. #10590279 | C3 | direct (N × H) |
| 20. C3×#870 | D3 | semidirect |
| 21. C3×#870 | C2×C3 | semidirect |
| 22. #63630 | C2×C3 | semidirect |
| 28. #63562 | C2×C3 | semidirect |
| 79. #870 | C3×D3 | semidirect |
| 189. C33 | #490 | semidirect |
| 285. C32 | #5067 | semidirect |
| 286. C32 | #5071 | semidirect |
| 287. C32 | C3×#490 | semidirect |
| 323. C3 | #10590279 | direct (N × H) |
| 324. C3 | C3×#5067 | semidirect |
| 325. C3 | C3×#5071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#874 | 2 |
| C32×#870 | 2 |
| C3×#63630 | 2 |
| C3×#63562 | 2 |
| C3×#5071 | 3 |
| C3×#5067 | 3 |
| #10590279 | 3 |