Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
649 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 649 conjugacy classes of subgroups — too many to draw. Only its 173 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. #11720530 | C2 | semidirect |
| 5. #11720529 | C2 | semidirect |
| 15. #88538 | C4 | semidirect |
| 31. #6180 | C2×C4 | semidirect |
| 114. H(3,𝔽3) | #428 | semidirect |
| 169. C32 | #4964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×H(3,𝔽3) | 2 |
| #11721826 | 2 |
| C2×#88538 | 2 |
| #11720530 | 2 |
| #11720529 | 2 |
| C3×#4964 | 3 |