Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
320 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 82 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×C9×C22⋊C8 | C2 | semidirect |
| 3. C3×C9⋊#95 | C2 | semidirect |
| 5. #10588147 | C3 | direct (N × H) |
| 9. C2×C3×D36 | C4 | semidirect |
| 12. C3×C4⋊Dic9 | C4 | semidirect |
| 18. C9×C22⋊C8 | C2×C3 | semidirect |
| 19. C9⋊#95 | C2×C3 | semidirect |
| 46. C2×D36 | C3×C4 | semidirect |
| 50. C4⋊Dic9 | C3×C4 | semidirect |
| 66. C3×C22⋊C8 | D9 | semidirect |
| 156. C22⋊C8 | C3×D9 | semidirect |
| 158. C3×C9 | #327 | semidirect |
| 247. C9 | C3×#327 | semidirect |
| 291. C3 | #10588147 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63492 | 2 |
| C3×C9×C22⋊C8 | 2 |
| C3×C9⋊#95 | 2 |
| C3×#4470 | 3 |
| #10588147 | 3 |