Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 1. C32×#919 | C2 | semidirect |
| 2. C3×#63807 | C2 | semidirect |
| 3. C3×#63656 | C2 | semidirect |
| 4. C32×#828 | C2 | semidirect |
| 5. C3×#63548 | C2 | semidirect |
| 6. C3×#63545 | C2 | semidirect |
| 7. C3×D3×C3⋊C16 | C2 | semidirect |
| 10. #10591046 | C3 | direct (N × H) |
| 24. C3×#919 | D3 | semidirect |
| 25. C3×#919 | C2×C3 | semidirect |
| 28. #63807 | C2×C3 | semidirect |
| 30. #63656 | C2×C3 | semidirect |
| 35. C3×#828 | D3 | semidirect |
| 36. C3×#828 | C2×C3 | semidirect |
| 43. #63548 | C2×C3 | semidirect |
| 44. #63545 | C2×C3 | semidirect |
| 45. D3×C3⋊C16 | C2×C3 | semidirect |
| 116. #919 | C3×D3 | semidirect |
| 129. #828 | C3×D3 | semidirect |
| 275. C33 | #508 | semidirect |
| 392. C32 | #4916 | semidirect |
| 393. C32 | #5194 | semidirect |
| 394. C32 | C3×#508 | semidirect |
| 436. C3 | #10591046 | direct (N × H) |
| 437. C3 | C3×#4916 | semidirect |
| 438. C3 | C3×#5194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#919 | 2 |
| C3×#63807 | 2 |
| C3×#63656 | 2 |
| C32×#828 | 2 |
| C3×#63548 | 2 |
| C3×#63545 | 2 |
| C3×D3×C3⋊C16 | 2 |
| C3×#5194 | 3 |
| C3×#4916 | 3 |
| #10591046 | 3 |