Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
263 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10589430 | C3 | semidirect |
| 8. Q16×H(3,𝔽3) | C4 | semidirect |
| 36. C32×Q16 | Dic3 | semidirect |
| 37. C32×Q16 | C3×C4 | semidirect |
| 123. H(3,𝔽3) | #358 | semidirect |
| 162. Q16 | (C3⋊Dic3)⋊C3 | semidirect |
| 186. C32 | #4564 | semidirect |
| 187. C32 | C3×#358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×H(3,𝔽3) | 2 |
| #63645⋊C3 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #10589430 | 3 |
| C3×#4564 | 3 |