Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
323 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10588703 | C3 | semidirect |
| 29. Q8×3−1+2 | Q8 | semidirect |
| 94. Q8×C9 | C3×Q8 | semidirect |
| 158. 3−1+2 | #477 | semidirect |
| 215. C9 | C3×#477 | semidirect |
| 218. Q8 | 3−1+2⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×3−1+2 | 2 |
| #63431⋊C3 | 2 |
| #63395⋊C3 | 2 |
| #63366⋊C3 | 2 |
| C4⋊(3−1+2⋊C8) | 2 |
| C3×#5021 | 3 |
| #10588703 | 3 |