Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
553 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 553 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×C3×#41⋊C9 | C2 | semidirect |
| 2. C3×#63692 | C2 | semidirect |
| 3. C3×#63691 | C2 | semidirect |
| 4. C3×#63690 | C2 | semidirect |
| 5. C3×#63689 | C2 | semidirect |
| 7. #10593098 | C3 | direct (N × H) |
| 10. C3×#41⋊C9 | C22 | semidirect |
| 11. C2×C3×Q8⋊C9 | C22 | semidirect |
| 12. C3×#3689 | C22 | semidirect |
| 13. C3×#3688 | C22 | semidirect |
| 26. C2×#41⋊C9 | C2×C3 | semidirect |
| 27. #63692 | C2×C3 | semidirect |
| 28. #63691 | C2×C3 | semidirect |
| 29. #63690 | C2×C3 | semidirect |
| 30. #63689 | C2×C3 | semidirect |
| 70. #41⋊C9 | C22×C3 | semidirect |
| 72. C2×Q8⋊C9 | C22×C3 | semidirect |
| 73. #3689 | C22×C3 | semidirect |
| 74. #3688 | C22×C3 | semidirect |
| 82. C2×C3×#41 | D9 | semidirect |
| 220. C2×#41 | C3×D9 | semidirect |
| 411. C3 | #10593098 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41⋊C9 | 2 |
| C3×#63692 | 2 |
| C3×#63691 | 2 |
| C3×#63690 | 2 |
| C3×#63689 | 2 |
| C3×#5822 | 3 |
| #10593098 | 3 |
| C3×#3697 | 4 |