Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
259 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 259 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×C16×H(3,𝔽3) | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C16))⋊C3 | C2 | semidirect |
| 4. #10589373 | C3 | semidirect |
| 16. C2×C32×C16 | D3 | semidirect |
| 17. C2×C32×C16 | C2×C3 | semidirect |
| 18. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 50. C2×(C3⋊D3)⋊C3 | C16 | semidirect |
| 116. C2×C3⋊D3 | C3×C16 | semidirect |
| 130. C2×C16 | (C3⋊D3)⋊C3 | semidirect |
| 131. H(3,𝔽3) | C22⋊C16 | semidirect |
| 202. C32 | (C2×D3)⋊C16 | semidirect |
| 203. C32 | C3×C22⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×(C3⋊D3)⋊C3 | 2 |
| C2×C16×H(3,𝔽3) | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #10589373 | 3 |
| C3×(C2×D3)⋊C16 | 3 |