Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1512 conjugacy classes of subgroups; only the 629 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 629 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 |
| 30. C32×Q16 | Dic3 | semidirect |
| 60. C3×Q16 | C3⋊Dic3 | semidirect |
| 78. C33 | #441 | semidirect |
| 90. Q16 | C3⋊(C3⋊Dic3) | semidirect |
| 103. C32 | #5184 | semidirect |
| 120. C3 | #10592883 | 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 |
| #11722187 | 2 |
| #11722185 | 2 |
| #10592883 | 3 |