Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
286 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 66 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. C3×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 4. C3×#63745 | C2 | semidirect |
| 5. C3×#63744 | C2 | semidirect |
| 6. #10593559 | C3 | direct (N × H) |
| 17. C4⋊PSU(3,𝔽2) | C2×C3 | semidirect |
| 19. #63745 | C2×C3 | semidirect |
| 20. #63744 | C2×C3 | semidirect |
| 28. C33×D4 | Q8 | semidirect |
| 30. C3×C4⋊(C3⋊D3) | Q8 | semidirect |
| 70. C32×D4 | C3×Q8 | semidirect |
| 72. C4⋊(C3⋊D3) | C3×Q8 | semidirect |
| 119. C33 | #476 | semidirect |
| 127. C3×D4 | PSU(3,𝔽2) | semidirect |
| 181. C32 | C3×#476 | semidirect |
| 186. D4 | C3×PSU(3,𝔽2) | semidirect |
| 219. C3 | #10593559 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×#157 | 2 |
| C3×C4⋊PSU(3,𝔽2) | 2 |
| C3×#63782 | 2 |
| C3×#63745 | 2 |
| C3×#63744 | 2 |
| #10593559 | 3 |
| C3×#476 | 9 |