Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
218 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 6. #10593532 | C3 | direct (N × H) |
| 28. C33×C8 | Q8 | semidirect |
| 29. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 63. C32×C8 | C3×Q8 | semidirect |
| 64. C3⋊(C3⋊C8) | C3×Q8 | semidirect |
| 95. C33 | #446 | semidirect |
| 108. C3×C8 | PSU(3,𝔽2) | semidirect |
| 138. C32 | C3×#446 | semidirect |
| 148. C8 | C3×PSU(3,𝔽2) | semidirect |
| 165. C3 | #10593532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×PSU(3,𝔽2) | 2 |
| C3×#63767 | 2 |
| C3×C8×#157 | 2 |
| C3×#63744 | 2 |
| #10593532 | 3 |
| C3×#446 | 9 |