Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
872 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 234 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 |
|---|---|---|
| 1. C33×C4⋊Q8 | C2 | semidirect |
| 3. C32×#810 | C2 | semidirect |
| 5. C32×#803 | C2 | semidirect |
| 7. C3×#5089 | C3 | direct (N × H) |
| 18. C32×C4⋊Q8 | D3 | semidirect |
| 19. C32×C4⋊Q8 | C2×C3 | semidirect |
| 25. C3×#810 | C2×C3 | semidirect |
| 27. C3×#803 | C2×C3 | semidirect |
| 39. #5089 | C32 | direct (N × H) |
| 72. C3×C4⋊Q8 | C3×D3 | semidirect |
| 73. C3×C4⋊Q8 | C2×C32 | semidirect |
| 79. #810 | C2×C32 | semidirect |
| 81. #803 | C2×C32 | semidirect |
| 157. C4⋊Q8 | C32×D3 | semidirect |
| 162. C33 | #489 | semidirect |
| 232. C32 | #5089 | direct (N × H) |
| 233. C32 | C3×#489 | semidirect |
| 265. C3 | C3×#5089 | direct (N × H) |
| 266. C3 | C32×#489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C32×#875 | 2 |
| C32×#810 | 2 |
| C32×#809 | 2 |
| C32×#803 | 2 |
| C32×#489 | 3 |
| C3×#5089 | 3 |