Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1221 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 1221 conjugacy classes of subgroups — too many to draw. Only its 265 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. #11721758 | C2 | semidirect |
| 5. #11721756 | C2 | semidirect |
| 7. C4×#6229 | C2 | semidirect |
| 32. C2×C4×H(3,𝔽3) | Q8 | semidirect |
| 82. C2×C32×C4 | Dic6 | semidirect |
| 141. H(3,𝔽3) | #533 | semidirect |
| 198. C32 | #5517 | semidirect |
| 205. C2×C4 | #6229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#117 | 2 |
| #11721826 | 2 |
| C2×C4×#1084 | 2 |
| #11721758 | 2 |
| #11721756 | 2 |
| #11721734 | 2 |
| C4×#6229 | 2 |
| C3×#5517 | 3 |