Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
830 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 144 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. C3×#64084 | C2 | semidirect |
| 2. C32×#874 | C2 | semidirect |
| 3. C2×C3×#3716 | C2 | semidirect |
| 4. C2×C3×#3714 | C2 | semidirect |
| 5. C32×#803 | C2 | semidirect |
| 8. #10590371 | C3 | direct (N × H) |
| 19. #64084 | C2×C3 | semidirect |
| 28. C3×#874 | D3 | semidirect |
| 29. C3×#874 | C2×C3 | semidirect |
| 30. C2×#3716 | C2×C3 | semidirect |
| 31. C2×#3714 | C2×C3 | semidirect |
| 34. C3×#803 | D3 | semidirect |
| 35. C3×#803 | C2×C3 | semidirect |
| 46. C32×C3⋊C8 | D4 | semidirect |
| 108. #874 | C3×D3 | semidirect |
| 112. #803 | C3×D3 | semidirect |
| 161. C3×C3⋊C8 | D12 | semidirect |
| 162. C3×C3⋊C8 | C3×D4 | semidirect |
| 251. C33 | #496 | semidirect |
| 301. C3⋊C8 | C3×D12 | semidirect |
| 378. C32 | #4712 | semidirect |
| 379. C32 | #5074 | semidirect |
| 380. C32 | C3×#496 | semidirect |
| 426. C3 | #10590371 | direct (N × H) |
| 427. C3 | C3×#4712 | semidirect |
| 428. C3 | C3×#5074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64084 | 2 |
| C32×#874 | 2 |
| C2×C3×#3716 | 2 |
| C2×C3×#3714 | 2 |
| C32×#803 | 2 |
| C3×#5074 | 3 |
| C3×#4712 | 3 |
| #10590371 | 3 |