Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2490 conjugacy classes of subgroups; only the 339 normal subgroups are shown.
This group has 2490 conjugacy classes of subgroups — too many to draw. Only its 339 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. C2×D4×C3⋊D9 | C2 | semidirect |
| 2. C3×C9×#127 | C2 | semidirect |
| 3. #11721840 | C2 | semidirect |
| 4. #11721711 | C2 | semidirect |
| 5. C42×C3⋊D9 | C2 | semidirect |
| 9. C2×C3×D4×C9 | C22 | semidirect |
| 10. C2×#6233 | C22 | semidirect |
| 12. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 14. C3×C42×C9 | C22 | semidirect |
| 15. C4×C3⋊Dic9 | C22 | semidirect |
| 22. C9×#127 | D3 | semidirect |
| 35. C4×C3⋊D9 | D4 | semidirect |
| 47. C2×D4×C9 | C2×D3 | semidirect |
| 52. C42×C9 | C2×D3 | semidirect |
| 59. C3×C4×C9 | C2×D4 | semidirect |
| 60. C3⋊Dic9 | C2×D4 | semidirect |
| 63. C3×#127 | D9 | semidirect |
| 95. C3⋊D9 | #127 | direct (N × H) |
| 98. C2×C3×D4 | C2×D9 | semidirect |
| 108. C3×C42 | C2×D9 | semidirect |
| 124. C4×C9 | D3×D4 | semidirect |
| 129. #127 | C3⋊D9 | direct (N × H) |
| 131. C3×C9 | C2×#127 | semidirect |
| 164. C2×D4 | C2×C3⋊D9 | semidirect |
| 167. C42 | C2×C3⋊D9 | semidirect |
| 178. C3×C4 | D4×D9 | semidirect |
| 183. C9 | D3×#127 | semidirect |
| 208. C4 | D4×C3⋊D9 | semidirect |
| 209. C3 | D9×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C3⋊D9 | 2 |
| C3×C9×#127 | 2 |
| #11721840 | 2 |
| #11721711 | 2 |
| C42×C3⋊D9 | 2 |
| C3⋊D3×#127 | 3 |
| D9×#127 | 3 |