Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1540 conjugacy classes of subgroups; only the 631 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 631 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 |
|---|---|---|
| 8. C33×Q16 | C4 | semidirect |
| 31. C32×Q16 | Dic3 | semidirect |
| 44. C3⋊(C3⋊Dic3) | Q16 | direct (N × H) |
| 64. C3×Q16 | C3⋊Dic3 | semidirect |
| 83. C33 | C4×Q16 | semidirect |
| 97. Q16 | C3⋊(C3⋊Dic3) | direct (N × H) |
| 111. C32 | Dic3×Q16 | semidirect |
| 131. C3 | Q16×C3⋊Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| Q8×C3⋊(C3⋊Dic3) | 2 |
| #11722205 | 2 |
| #11722188 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| Q16×C3⋊Dic3 | 3 |