Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
980 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 184 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. #11723501 | C2 | semidirect |
| 3. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C32×#818 | C2 | semidirect |
| 5. #11722033 | C2 | semidirect |
| 13. C3×#3745 | C4 | semidirect |
| 25. C3×#818 | D3 | semidirect |
| 32. C3×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 35. C33×C8 | C2×C4 | semidirect |
| 54. #3745 | Dic3 | semidirect |
| 65. C3⋊(C3⋊Dic3) | D8 | semidirect |
| 73. #818 | C3⋊D3 | semidirect |
| 91. C4⋊(C3⋊D3) | C2×Dic3 | semidirect |
| 98. C32×C8 | C4×D3 | semidirect |
| 99. C32×C8 | C2×Dic3 | semidirect |
| 155. C33 | C4×D8 | semidirect |
| 176. C3×C8 | D3×Dic3 | semidirect |
| 177. C3×C8 | C4×C3⋊D3 | semidirect |
| 224. C32 | #4872 | semidirect |
| 225. C32 | Dic3×D8 | semidirect |
| 235. C8 | Dic3×C3⋊D3 | semidirect |
| 257. C3 | #10590777 | semidirect |
| 258. C3 | #10592571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3745 | 2 |
| #11723501 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| C32×#818 | 2 |
| #11722033 | 2 |
| #10592571 | 3 |
| #10590777 | 3 |