Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1108 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 1108 conjugacy classes of subgroups — too many to draw. Only its 180 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. #11723494 | C2 | semidirect |
| 3. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 4. C32×#818 | C2 | semidirect |
| 5. #11722035 | C2 | semidirect |
| 11. #88852 | C4 | semidirect |
| 22. C8×C3⋊Dic3 | D3 | semidirect |
| 24. C3×#818 | D3 | semidirect |
| 30. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 35. C33×C8 | C2×C4 | semidirect |
| 65. C3×C3⋊Dic3 | D8 | semidirect |
| 75. #818 | C3⋊D3 | semidirect |
| 99. C32×C8 | C4×D3 | semidirect |
| 100. C32×C8 | C4×D3 | semidirect |
| 147. C3⋊Dic3 | D24 | semidirect |
| 156. C33 | C4×D8 | semidirect |
| 179. C3×C8 | #624 | semidirect |
| 180. C3×C8 | C4×C3⋊D3 | semidirect |
| 227. C32 | C4×D24 | semidirect |
| 228. C32 | #4872 | semidirect |
| 238. C8 | #6289 | semidirect |
| 261. C3 | #10590763 | semidirect |
| 262. C3 | #10592571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88852 | 2 |
| #11723494 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| C32×#818 | 2 |
| #11722035 | 2 |
| #10592571 | 3 |
| #10590763 | 3 |