Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1602 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 213 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×#88646 | C2 | semidirect |
| 2. C42×C3⋊D9 | C2 | semidirect |
| 3. C9×#874 | C2 | semidirect |
| 4. C3×#63436 | C2 | semidirect |
| 5. #11721043 | C2 | semidirect |
| 10. C2×C9×D12 | C22 | semidirect |
| 11. C2×C3×D36 | C22 | semidirect |
| 12. C2×#6194 | C22 | semidirect |
| 14. C3×C42×C9 | C22 | semidirect |
| 15. C4×C3⋊Dic9 | C22 | semidirect |
| 24. #63436 | D3 | semidirect |
| 33. C4×C3⋊D9 | D4 | semidirect |
| 51. C2×D36 | C2×D3 | semidirect |
| 55. C42×C9 | C2×D3 | semidirect |
| 63. C3×C4×C9 | C2×D4 | semidirect |
| 64. C3⋊Dic9 | C2×D4 | semidirect |
| 72. #874 | D9 | semidirect |
| 102. C3⋊D9 | #127 | semidirect |
| 114. C2×D12 | C2×D9 | semidirect |
| 119. C3×C42 | C2×D9 | semidirect |
| 139. C4×C9 | D3×D4 | semidirect |
| 147. C3×C9 | C2×#127 | semidirect |
| 189. C42 | D3×D9 | semidirect |
| 203. C3×C4 | D4×D9 | semidirect |
| 210. C9 | D3×#127 | semidirect |
| 237. C4 | #88646 | semidirect |
| 239. C3 | D9×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88646 | 2 |
| C42×C3⋊D9 | 2 |
| C9×#874 | 2 |
| C3×#63436 | 2 |
| #11721043 | 2 |
| #10594008 | 3 |
| D9×#127 | 3 |