Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. C3×C9×Q32 | C2 | semidirect |
| 3. #11720568 | C2 | semidirect |
| 4. #11720509 | C2 | semidirect |
| 21. C9×Q32 | D3 | semidirect |
| 55. C3×Q32 | D9 | semidirect |
| 79. C3⋊D9 | Q32 | direct (N × H) |
| 107. Q32 | C3⋊D9 | direct (N × H) |
| 109. C3×C9 | C2×Q32 | semidirect |
| 146. C9 | D3×Q32 | semidirect |
| 163. C3 | D9×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×C3⋊D9 | 2 |
| C3×C9×Q32 | 2 |
| #11720568 | 2 |
| #11720509 | 2 |
| C16×C3⋊D9 | 2 |
| C3⋊D3×Q32 | 3 |
| D9×Q32 | 3 |