Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1276 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1276 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×#89022 | C2 | semidirect |
| 2. C2×#88860 | C2 | semidirect |
| 3. C2×C3×#3754 | C2 | semidirect |
| 4. C32×#938 | C2 | semidirect |
| 5. #11722039 | C2 | semidirect |
| 6. #11722035 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 28. C2×#3754 | D3 | semidirect |
| 32. C3×#938 | D3 | semidirect |
| 47. C4⋊(C3⋊(C3⋊D3)) | D4 | semidirect |
| 50. C3×#634 | D4 | semidirect |
| 115. #938 | C3⋊D3 | semidirect |
| 158. #634 | #67 | semidirect |
| 261. C33 | #449 | semidirect |
| 382. C32 | #5037 | semidirect |
| 383. C32 | #5172 | semidirect |
| 437. C3 | #10591521 | semidirect |
| 438. C3 | #10592736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89022 | 2 |
| C2×#88860 | 2 |
| C2×C3×#3754 | 2 |
| C32×#938 | 2 |
| #11722039 | 2 |
| #11722035 | 2 |
| (C2×D3)⋊(C3⋊(C3⋊C8)) | 2 |
| #10592736 | 3 |
| #10591521 | 3 |