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. #10588535 | C3 | semidirect |
| 31. C8×3−1+2 | Q8 | semidirect |
| 32. 3−1+2⋊C8 | Q8 | semidirect |
| 82. C8×C9 | C3×Q8 | semidirect |
| 83. C9⋊C8 | C3×Q8 | semidirect |
| 122. 3−1+2 | #498 | semidirect |
| 164. C9 | C3×#498 | semidirect |
| 171. 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×#106 | 2 |
| #63377⋊C3 | 2 |
| C8×3−1+2⋊C4 | 2 |
| #63367⋊C3 | 2 |
| C3×#4855 | 3 |
| #10588535 | 3 |