Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1020 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 198 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. C2×C33×Q16 | C2 | semidirect |
| 2. C3×#64156 | C2 | semidirect |
| 3. C2×C3×#3755 | C2 | semidirect |
| 5. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 6. #10592890 | C3 | direct (N × H) |
| 18. C2×C32×Q16 | D3 | semidirect |
| 19. C2×C32×Q16 | C2×C3 | semidirect |
| 20. #64156 | C2×C3 | semidirect |
| 21. C2×#3755 | C2×C3 | semidirect |
| 26. C8×C3⋊Dic3 | C2×C3 | semidirect |
| 69. C2×C3×Q16 | C3×D3 | semidirect |
| 70. C2×C3×Q16 | C3⋊D3 | semidirect |
| 147. C2×Q16 | C3×C3⋊D3 | semidirect |
| 152. C33 | #495 | semidirect |
| 214. C32 | #5191 | semidirect |
| 215. C32 | C3×#495 | semidirect |
| 242. C3 | C3×#5191 | semidirect |
| 243. C3 | #10592890 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| C3×#64156 | 2 |
| C2×C3×#3755 | 2 |
| C2×C3×#3745 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| #10592890 | 3 |
| C3×#5191 | 3 |