Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
341 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 186 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. Q8×C9⋊C8 | C3 | semidirect |
| 18. Q8×3−1+2 | C8 | semidirect |
| 23. 3−1+2⋊C8 | Q8 | direct (N × H) |
| 57. Q8×C9 | C3×C8 | semidirect |
| 65. C9⋊C8 | C3×Q8 | semidirect |
| 98. 3−1+2 | C8×Q8 | semidirect |
| 137. C9 | C3×C8×Q8 | semidirect |
| 138. Q8 | 3−1+2⋊C8 | direct (N × H) |
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 |
| C4⋊(3−1+2⋊C8) | 2 |
| C4×3−1+2⋊C8 | 2 |
| C3×Q8×C3⋊C8 | 3 |
| Q8×C9⋊C8 | 3 |