Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
301 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 301 conjugacy classes of subgroups — too many to draw. Only its 122 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. #10588509 | C3 | semidirect |
| 35. 3−1+2⋊C8 | Q8 | semidirect |
| 94. C9⋊C8 | C3×Q8 | semidirect |
| 139. 3−1+2 | #446 | semidirect |
| 191. C9 | C3×#446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×3−1+2⋊Q8 | 2 |
| 3−1+2×C4⋊C8 | 2 |
| #63375⋊C3 | 2 |
| (3−1+2⋊C4)⋊C8 | 2 |
| C4×3−1+2⋊C8 | 2 |
| C3×#4831 | 3 |
| #10588509 | 3 |