Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
649 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 649 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #11721715 | C2 | semidirect |
| 3. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 4. #11720554 | C2 | semidirect |
| 16. C32×C4×C8 | D3 | semidirect |
| 96. C4×C8 | #272 | semidirect |
| 97. H(3,𝔽3) | #486 | semidirect |
| 146. C32 | #4694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721720 | 2 |
| #11721715 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #11720554 | 2 |
| C3×#4694 | 3 |