Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 419 normal subgroups are shown.
This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 419 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 |
|---|---|---|
| 4. C33×C4⋊C8 | C2 | semidirect |
| 5. #11722184 | C2 | semidirect |
| 6. #11722184 | C2 | semidirect |
| 7. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 25. C32×C4⋊C8 | D3 | semidirect |
| 70. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 122. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 123. C33 | #424 | semidirect |
| 165. C32 | #4839 | semidirect |
| 194. C3 | #10592538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88850 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11723913 | 2 |
| C33×C4⋊C8 | 2 |
| #11722184 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592538 | 3 |