Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
820 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 190 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. C3×#64079 | C2 | semidirect |
| 3. C33×#97 | C2 | semidirect |
| 4. C3×#63648 | C2 | semidirect |
| 5. #10592412 | C3 | direct (N × H) |
| 14. #64079 | C2×C3 | semidirect |
| 18. C32×#97 | D3 | semidirect |
| 19. C32×#97 | C2×C3 | semidirect |
| 20. #63648 | C2×C3 | semidirect |
| 57. C3×#97 | C3×D3 | semidirect |
| 58. C3×#97 | C3⋊D3 | semidirect |
| 113. #97 | C3×C3⋊D3 | semidirect |
| 114. C33 | #490 | semidirect |
| 162. C32 | #4713 | semidirect |
| 163. C32 | C3×#490 | semidirect |
| 186. C3 | C3×#4713 | semidirect |
| 187. C3 | #10592412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64083 | 2 |
| C3×#64079 | 2 |
| C33×#97 | 2 |
| C3×#63648 | 2 |
| #10592412 | 3 |
| C3×#4713 | 3 |