Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2100 conjugacy classes of subgroups; only the 851 normal subgroups are shown.
This group has 2100 conjugacy classes of subgroups — too many to draw. Only its 851 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 |
|---|---|---|
| 4. #11722205 | C2 | semidirect |
| 8. C2×C33×Q8 | C4 | semidirect |
| 36. C2×C32×Q8 | Dic3 | semidirect |
| 75. C2×C3×Q8 | C3⋊Dic3 | semidirect |
| 96. C33 | #419 | semidirect |
| 114. C2×Q8 | C3⋊(C3⋊Dic3) | semidirect |
| 131. C32 | #5225 | semidirect |
| 155. C3 | #10592924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| #11723967 | 2 |
| C2×#88855 | 2 |
| #11722205 | 2 |
| #10592924 | 3 |