Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
884 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 884 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 |
|---|---|---|
| 1. C33×#125 | C2 | semidirect |
| 3. C3×#63636 | C2 | semidirect |
| 4. C3×#63630 | C2 | semidirect |
| 5. #10592766 | C3 | direct (N × H) |
| 14. C32×#125 | D3 | semidirect |
| 15. C32×#125 | C2×C3 | semidirect |
| 18. #63636 | C2×C3 | semidirect |
| 19. #63630 | C2×C3 | semidirect |
| 54. C3×#125 | C3×D3 | semidirect |
| 55. C3×#125 | C3⋊D3 | semidirect |
| 114. #125 | C3×C3⋊D3 | semidirect |
| 117. C33 | #490 | semidirect |
| 166. C32 | #5067 | semidirect |
| 167. C32 | C3×#490 | semidirect |
| 190. C3 | C3×#5067 | semidirect |
| 191. C3 | #10592766 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#125 | 2 |
| C3×#64083 | 2 |
| C3×#63636 | 2 |
| C3×#63630 | 2 |
| #10592766 | 3 |
| C3×#5067 | 3 |