Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1244 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 158 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×#89021 | C2 | semidirect |
| 2. C2×#88861 | C2 | semidirect |
| 3. C2×C3×#3753 | C2 | semidirect |
| 4. C32×#938 | C2 | semidirect |
| 5. #11722041 | C2 | semidirect |
| 6. #11722033 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 31. C2×#3753 | D3 | semidirect |
| 32. C3×#938 | D3 | semidirect |
| 48. #6308 | D4 | semidirect |
| 50. C3×C4⋊(C3⋊D3) | D4 | semidirect |
| 115. #938 | C3⋊D3 | semidirect |
| 152. C4⋊(C3⋊D3) | #67 | semidirect |
| 259. C33 | #449 | semidirect |
| 377. C32 | #5037 | semidirect |
| 378. C32 | #5158 | semidirect |
| 431. C3 | #10591519 | semidirect |
| 432. C3 | #10592736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89021 | 2 |
| C2×#88861 | 2 |
| C2×C3×#3753 | 2 |
| C32×#938 | 2 |
| #11722041 | 2 |
| #11722033 | 2 |
| (C2×D3)⋊(C3⋊(C3⋊C8)) | 2 |
| #10592736 | 3 |
| #10591519 | 3 |