Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
349 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 100 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. #63450⋊C3 | C2 | semidirect |
| 5. #63378⋊C3 | C2 | semidirect |
| 6. (3−1+2⋊C4)⋊C8 | C2 | semidirect |
| 7. #63366⋊C3 | C2 | semidirect |
| 9. #10588439 | C3 | semidirect |
| 29. #63450 | C2×C3 | semidirect |
| 33. #63378 | C2×C3 | semidirect |
| 34. Dic9⋊C8 | C2×C3 | semidirect |
| 35. #63366 | C2×C3 | semidirect |
| 38. D4×3−1+2 | Q8 | semidirect |
| 119. D4×C9 | C3×Q8 | semidirect |
| 196. 3−1+2 | #474 | semidirect |
| 270. C9 | C3×#474 | semidirect |
| 274. D4 | 3−1+2⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×3−1+2⋊C4 | 2 |
| #63450⋊C3 | 2 |
| 3−1+2×#102 | 2 |
| #63392⋊C3 | 2 |
| #63378⋊C3 | 2 |
| (3−1+2⋊C4)⋊C8 | 2 |
| #63366⋊C3 | 2 |
| C3×#4759 | 3 |
| #10588439 | 3 |