Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 2. D4×3−1+2⋊C4 | C2 | semidirect |
| 3. #63392⋊C3 | C2 | semidirect |
| 4. #63378⋊C3 | C2 | semidirect |
| 5. C8×3−1+2⋊C4 | C2 | semidirect |
| 7. D8×Dic9 | C3 | semidirect |
| 10. D8×3−1+2 | C4 | semidirect |
| 23. D4×Dic9 | C2×C3 | semidirect |
| 24. #63392 | C2×C3 | semidirect |
| 25. #63378 | C2×C3 | semidirect |
| 26. C8×Dic9 | C2×C3 | semidirect |
| 29. D4×3−1+2 | C2×C4 | semidirect |
| 35. C8×3−1+2 | C2×C4 | semidirect |
| 51. C9×D8 | C3×C4 | semidirect |
| 66. 3−1+2⋊C4 | D8 | direct (N × H) |
| 92. D4×C9 | C2×C3×C4 | semidirect |
| 100. C8×C9 | C2×C3×C4 | semidirect |
| 146. Dic9 | C3×D8 | semidirect |
| 152. 3−1+2 | C4×D8 | semidirect |
| 187. D8 | 3−1+2⋊C4 | direct (N × H) |
| 213. C9 | C3×C4×D8 | semidirect |
| 216. D4 | C2×3−1+2⋊C4 | semidirect |
| 223. C8 | C2×3−1+2⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×3−1+2 | 2 |
| D4×3−1+2⋊C4 | 2 |
| #63392⋊C3 | 2 |
| #63378⋊C3 | 2 |
| C8×3−1+2⋊C4 | 2 |
| C3×Dic3×D8 | 3 |
| D8×Dic9 | 3 |