Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
312 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 7. #10588554 | C3 | semidirect |
| 32. C8×3−1+2 | Q8 | semidirect |
| 33. 3−1+2⋊C8 | Q8 | semidirect |
| 86. C8×C9 | C3×Q8 | semidirect |
| 87. C9⋊C8 | C3×Q8 | semidirect |
| 129. 3−1+2 | #500 | semidirect |
| 178. C9 | C3×#500 | semidirect |
| 186. C8 | 3−1+2⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63450⋊C3 | 2 |
| 3−1+2×#107 | 2 |
| #63378⋊C3 | 2 |
| C8×3−1+2⋊C4 | 2 |
| #63366⋊C3 | 2 |
| C3×#4874 | 3 |
| #10588554 | 3 |