Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1540 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 469 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. C33×C4⋊C8 | C2 | semidirect |
| 4. #11722185 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 17. C32×C4⋊C8 | D3 | semidirect |
| 56. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 100. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 103. C33 | #432 | semidirect |
| 141. C32 | #4835 | semidirect |
| 170. C3 | #10592534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C3⋊(C3⋊D3) | 2 |
| C33×C4⋊C8 | 2 |
| #11722190 | 2 |
| #11722185 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592534 | 3 |