Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1024 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 238 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×#3745 | C2 | semidirect |
| 2. C2×C3×#3744 | C2 | semidirect |
| 3. C3×#64084 | C2 | semidirect |
| 4. C3×#64083 | C2 | semidirect |
| 5. C33×#97 | C2 | semidirect |
| 6. #10592411 | C3 | direct (N × H) |
| 17. C2×#3745 | C2×C3 | semidirect |
| 18. C2×#3744 | C2×C3 | semidirect |
| 19. #64084 | C2×C3 | semidirect |
| 20. #64083 | C2×C3 | semidirect |
| 26. C32×#97 | D3 | semidirect |
| 27. C32×#97 | C2×C3 | semidirect |
| 38. C33×C8 | D4 | semidirect |
| 78. C3×#97 | C3×D3 | semidirect |
| 79. C3×#97 | C3⋊D3 | semidirect |
| 103. C32×C8 | D12 | semidirect |
| 104. C32×C8 | C3×D4 | semidirect |
| 153. #97 | C3×C3⋊D3 | semidirect |
| 154. C33 | #496 | semidirect |
| 178. C3×C8 | C3×D12 | semidirect |
| 179. C3×C8 | C4⋊(C3⋊D3) | semidirect |
| 219. C32 | #4712 | semidirect |
| 220. C32 | C3×#496 | semidirect |
| 231. C8 | C3×C4⋊(C3⋊D3) | semidirect |
| 251. C3 | C3×#4712 | semidirect |
| 252. C3 | #10592411 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3745 | 2 |
| C2×C3×#3744 | 2 |
| C3×#64084 | 2 |
| C3×#64083 | 2 |
| C33×#97 | 2 |
| #10592411 | 3 |
| C3×#4712 | 3 |