Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
267 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 70 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. H(3,𝔽3)×#107 | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C16))⋊C3 | C2 | semidirect |
| 4. #10589357 | C3 | semidirect |
| 10. #3745⋊C3 | C4 | semidirect |
| 15. C32×#107 | D3 | semidirect |
| 16. C32×#107 | C2×C3 | semidirect |
| 17. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 38. #3745 | C3×C4 | semidirect |
| 123. #107 | (C3⋊D3)⋊C3 | semidirect |
| 124. H(3,𝔽3) | #357 | semidirect |
| 193. C32 | #4491 | semidirect |
| 194. C32 | C3×#357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745⋊C3 | 2 |
| H(3,𝔽3)×#107 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #10589357 | 3 |
| C3×#4491 | 3 |