Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
733 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 733 conjugacy classes of subgroups — too many to draw. Only its 148 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×M16×H(3,𝔽3) | C2 | semidirect |
| 3. #64135⋊C3 | C2 | semidirect |
| 4. #63648⋊C3 | C2 | semidirect |
| 5. #10592830 | C3 | semidirect |
| 11. C2×C4⋊((C3⋊D3)⋊C3) | C4 | semidirect |
| 14. C2×C8×H(3,𝔽3) | C22 | semidirect |
| 16. C4⋊((C3⋊Dic3)⋊C3) | C22 | semidirect |
| 21. C2×C32×M16 | D3 | semidirect |
| 22. C2×C32×M16 | C2×C3 | semidirect |
| 23. #64135 | C2×C3 | semidirect |
| 25. #63648 | C2×C3 | semidirect |
| 50. C2×C4⋊(C3⋊D3) | C3×C4 | semidirect |
| 60. C2×C32×C8 | C2×D3 | semidirect |
| 61. C2×C32×C8 | C22×C3 | semidirect |
| 63. C4⋊(C3⋊Dic3) | C22×C3 | semidirect |
| 191. C2×M16 | (C3⋊D3)⋊C3 | semidirect |
| 194. H(3,𝔽3) | #418 | semidirect |
| 258. C2×C8 | C2×(C3⋊D3)⋊C3 | semidirect |
| 299. C32 | #5131 | semidirect |
| 300. C32 | C3×#418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊((C3⋊D3)⋊C3) | 2 |
| C2×M16×H(3,𝔽3) | 2 |
| #64135⋊C3 | 2 |
| #63648⋊C3 | 2 |
| #10592830 | 3 |
| C3×#5131 | 3 |