Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1016 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1016 conjugacy classes of subgroups — too many to draw. Only its 258 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 |
| 2. C2×C32×#216 | C2 | semidirect |
| 5. C32×#803 | C2 | semidirect |
| 7. C3×#5086 | C3 | direct (N × H) |
| 20. C32×C4⋊Q8 | D3 | semidirect |
| 21. C32×C4⋊Q8 | C2×C3 | semidirect |
| 23. C2×C3×#216 | C2×C3 | semidirect |
| 27. C3×#803 | C2×C3 | semidirect |
| 39. #5086 | C32 | direct (N × H) |
| 71. C3×C4⋊Q8 | C3×D3 | semidirect |
| 72. C3×C4⋊Q8 | C2×C32 | semidirect |
| 74. C2×#216 | C2×C32 | semidirect |
| 78. #803 | C2×C32 | semidirect |
| 149. C4⋊Q8 | C32×D3 | semidirect |
| 152. C33 | #497 | semidirect |
| 214. C32 | #5086 | direct (N × H) |
| 215. C32 | C3×#497 | semidirect |
| 242. C3 | C3×#5086 | direct (N × H) |
| 243. C3 | C32×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C2×C32×#216 | 2 |
| C2×C32×#215 | 2 |
| C32×#875 | 2 |
| C32×#803 | 2 |
| C32×#497 | 3 |
| C3×#5086 | 3 |