Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
192 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. C8×Q8⋊C9 | C3 | semidirect |
| 11. #6204 | C8 | direct (N × H) |
| 39. Q8⋊C9 | C3×C8 | semidirect |
| 41. C8×Q8 | 3−1+2 | semidirect |
| 108. Q8 | C8×3−1+2 | semidirect |
| 113. C8 | #6204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6204 | 2 |
| C32×C8×Q8 | 3 |
| C8×Q8⋊C9 | 3 |
| C2×C8×3−1+2 | 4 |