Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
210 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 210 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 |
|---|---|---|
| 8. #10593537 | C3 | direct (N × H) |
| 35. C3×#622 | Q8 | semidirect |
| 36. C33×C8 | Q8 | semidirect |
| 37. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 76. #622 | C3×Q8 | semidirect |
| 79. C32×C8 | C3×Q8 | semidirect |
| 80. C3⋊(C3⋊C8) | C3×Q8 | semidirect |
| 118. C33 | #501 | semidirect |
| 132. C3×C8 | PSU(3,𝔽2) | semidirect |
| 167. C32 | C3×#501 | semidirect |
| 178. C8 | C3×PSU(3,𝔽2) | semidirect |
| 197. C3 | #10593537 | 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×#64243 | 2 |
| C3×#63769 | 2 |
| C3×#63768 | 2 |
| C3×#63767 | 2 |
| C3×#63746 | 2 |
| C3×#63745 | 2 |
| #10593537 | 3 |
| C3×#501 | 9 |