Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
226 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 5. #10593536 | C3 | direct (N × H) |
| 21. C3×#622 | Q8 | semidirect |
| 22. C33×C8 | Q8 | semidirect |
| 23. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 48. #622 | C3×Q8 | semidirect |
| 51. C32×C8 | C3×Q8 | semidirect |
| 52. C3⋊(C3⋊C8) | C3×Q8 | semidirect |
| 79. C33 | #500 | semidirect |
| 90. C3×C8 | PSU(3,𝔽2) | semidirect |
| 117. C32 | C3×#500 | semidirect |
| 125. C8 | C3×PSU(3,𝔽2) | semidirect |
| 141. C3 | #10593536 | 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×#63769 | 2 |
| C3×C8×#157 | 2 |
| C3×#63746 | 2 |
| #10593536 | 3 |
| C3×#500 | 9 |