Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
204 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 5. #10588241 | C3 | semidirect |
| 8. Q16×3−1+2 | C4 | semidirect |
| 39. C9×Q16 | C3×C4 | semidirect |
| 108. 3−1+2 | #358 | semidirect |
| 134. Q16 | 3−1+2⋊C4 | semidirect |
| 150. C9 | C3×#358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×3−1+2 | 2 |
| #63378⋊C3 | 2 |
| C2×3−1+2⋊C16 | 2 |
| C3×#4564 | 3 |
| #10588241 | 3 |