Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
472 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 2. C2×#3744⋊C3 | C2 | semidirect |
| 3. #64084⋊C3 | C2 | semidirect |
| 4. C4×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 5. H(3,𝔽3)×C4⋊C8 | C2 | semidirect |
| 6. #63648⋊C3 | C2 | semidirect |
| 7. #63643⋊C3 | C2 | semidirect |
| 8. #10592543 | C3 | semidirect |
| 24. C2×#3744 | C2×C3 | semidirect |
| 25. #64084 | C2×C3 | semidirect |
| 26. C4×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 32. C32×C4⋊C8 | D3 | semidirect |
| 33. C32×C4⋊C8 | C2×C3 | semidirect |
| 34. #63648 | C2×C3 | semidirect |
| 35. #63643 | C2×C3 | semidirect |
| 241. C4⋊C8 | (C3⋊D3)⋊C3 | semidirect |
| 244. H(3,𝔽3) | #463 | semidirect |
| 369. C32 | #4844 | semidirect |
| 370. C32 | C3×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745⋊C3 | 2 |
| C2×#3744⋊C3 | 2 |
| #64084⋊C3 | 2 |
| C4×C4⋊((C3⋊D3)⋊C3) | 2 |
| H(3,𝔽3)×C4⋊C8 | 2 |
| #63648⋊C3 | 2 |
| #63643⋊C3 | 2 |
| #10592543 | 3 |
| C3×#4844 | 3 |