Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
428 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 96 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×D8×3−1+2 | C2 | semidirect |
| 2. #63500⋊C3 | C2 | semidirect |
| 3. C2×#3663⋊C3 | C2 | semidirect |
| 4. #63392⋊C3 | C2 | semidirect |
| 5. #63377⋊C3 | C2 | semidirect |
| 7. #10588839 | C3 | semidirect |
| 23. C2×C9×D8 | C2×C3 | semidirect |
| 24. #63500 | C2×C3 | semidirect |
| 25. C2×#3663 | C2×C3 | semidirect |
| 26. #63392 | C2×C3 | semidirect |
| 27. #63377 | C2×C3 | semidirect |
| 38. C8×3−1+2 | D4 | semidirect |
| 110. C8×C9 | C3×D4 | semidirect |
| 161. C2×D8 | AGL(1,ℤ/9) | semidirect |
| 166. 3−1+2 | #469 | semidirect |
| 233. C9 | C3×#469 | semidirect |
| 245. C8 | #611⋊C3 | 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 |
| #63500⋊C3 | 2 |
| C2×#3663⋊C3 | 2 |
| #63392⋊C3 | 2 |
| #63377⋊C3 | 2 |
| C3×#5159 | 3 |
| #10588839 | 3 |