Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
660 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. C4×#6229 | C2 | semidirect |
| 5. #11720532 | C2 | semidirect |
| 6. #11720529 | C2 | semidirect |
| 7. #11720520 | C2 | semidirect |
| 15. #88546 | C4 | semidirect |
| 39. #6229 | C2×C4 | semidirect |
| 41. #6180 | C2×C4 | semidirect |
| 142. H(3,𝔽3) | #440 | semidirect |
| 209. C32 | #5018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×H(3,𝔽3) | 2 |
| C2×#88546 | 2 |
| C4×#6229 | 2 |
| #11720578 | 2 |
| #11720532 | 2 |
| #11720529 | 2 |
| #11720520 | 2 |
| C3×#5018 | 3 |