Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 405 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 |
|---|---|---|
| 1. C2×C33×SD16 | C2 | semidirect |
| 2. #11723988 | C2 | semidirect |
| 3. D4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 5. #11722205 | C2 | semidirect |
| 6. #11722191 | C2 | semidirect |
| 7. #11722184 | C2 | semidirect |
| 22. C2×C32×SD16 | D3 | semidirect |
| 72. C2×C3×SD16 | C3⋊D3 | semidirect |
| 127. C2×SD16 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #463 | semidirect |
| 182. C32 | #5165 | semidirect |
| 217. C3 | #10592864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×SD16 | 2 |
| #11723988 | 2 |
| D4×C3⋊(C3⋊Dic3) | 2 |
| C2×#88860 | 2 |
| #11722205 | 2 |
| #11722191 | 2 |
| #11722184 | 2 |
| #10592864 | 3 |