Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1276 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 1276 conjugacy classes of subgroups — too many to draw. Only its 206 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×C33×D8 | C2 | semidirect |
| 2. C3×#64149 | C2 | semidirect |
| 3. C2×C3×#3753 | C2 | semidirect |
| 4. C2×C3×#3745 | C2 | semidirect |
| 5. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 6. #10592850 | C3 | direct (N × H) |
| 18. C2×C32×D8 | D3 | semidirect |
| 19. C2×C32×D8 | C2×C3 | semidirect |
| 20. #64149 | C2×C3 | semidirect |
| 21. C2×#3753 | C2×C3 | semidirect |
| 22. C2×#3745 | C2×C3 | semidirect |
| 26. C8×C3⋊Dic3 | C2×C3 | semidirect |
| 37. C33×C8 | D4 | semidirect |
| 38. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 69. C3×C3⋊Dic3 | D8 | semidirect |
| 73. C2×C3×D8 | C3×D3 | semidirect |
| 74. C2×C3×D8 | C3⋊D3 | semidirect |
| 104. C32×C8 | #67 | semidirect |
| 105. C32×C8 | C3×D4 | semidirect |
| 106. C3⋊(C3⋊C8) | C3×D4 | semidirect |
| 153. C3⋊Dic3 | C3×D8 | semidirect |
| 157. C2×D8 | C3×C3⋊D3 | semidirect |
| 160. C33 | #493 | semidirect |
| 185. C3×C8 | C3×#67 | semidirect |
| 186. C3×C8 | #638 | semidirect |
| 230. C32 | #5151 | semidirect |
| 231. C32 | C3×#493 | semidirect |
| 242. C8 | C3×#638 | semidirect |
| 263. C3 | C3×#5151 | semidirect |
| 264. C3 | #10592850 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| C3×#64149 | 2 |
| C2×C3×#3753 | 2 |
| C2×C3×#3745 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| #10592850 | 3 |
| C3×#5151 | 3 |