Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1428 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 1428 conjugacy classes of subgroups — too many to draw. Only its 405 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. #11723911 | C2 | semidirect |
| 3. C33×C4⋊C8 | C2 | semidirect |
| 6. #11722188 | C2 | semidirect |
| 7. #11722187 | C2 | semidirect |
| 22. C32×C4⋊C8 | D3 | semidirect |
| 64. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 112. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 115. C33 | #478 | semidirect |
| 154. C32 | #4847 | semidirect |
| 182. C3 | #10592546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11723911 | 2 |
| C33×C4⋊C8 | 2 |
| #11722191 | 2 |
| #11722188 | 2 |
| #11722187 | 2 |
| #10592546 | 3 |