Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
323 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 59 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. #11720775 | C2 | semidirect |
| 4. #11720774 | C2 | semidirect |
| 9. C2×C8×H(3,𝔽3) | C4 | semidirect |
| 10. C2×#6180 | C4 | semidirect |
| 11. C8×#272 | C4 | semidirect |
| 12. C8×#272 | C4 | semidirect |
| 95. H(3,𝔽3) | #427 | semidirect |
| 129. C2×C8 | #1088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722448 | 2 |
| C2×C8×#272 | 2 |
| #11720775 | 2 |
| #11720774 | 2 |
| C3×#427 | 9 |