Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
355 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 6. #10592401 | C3 | semidirect |
| 35. C8×H(3,𝔽3) | Q8 | semidirect |
| 100. C32×C8 | Dic6 | semidirect |
| 101. C32×C8 | C3×Q8 | semidirect |
| 158. H(3,𝔽3) | #501 | semidirect |
| 231. C32 | #4702 | semidirect |
| 232. C32 | C3×#501 | semidirect |
| 240. C8 | #634⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64079⋊C3 | 2 |
| #64078⋊C3 | 2 |
| H(3,𝔽3)×#97 | 2 |
| #63645⋊C3 | 2 |
| #63644⋊C3 | 2 |
| #10592401 | 3 |
| C3×#4702 | 3 |