Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1568 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 459 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. C33×C4×Q8 | C2 | semidirect |
| 2. C2×#88863 | C2 | semidirect |
| 5. #11722180 | C2 | semidirect |
| 7. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 22. C32×C4×Q8 | D3 | semidirect |
| 69. C3×C4×Q8 | C3⋊D3 | semidirect |
| 123. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 127. C33 | #464 | semidirect |
| 171. C32 | #5028 | semidirect |
| 202. C3 | #10592727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×Q8 | 2 |
| C2×#88863 | 2 |
| C2×#88862 | 2 |
| #11723916 | 2 |
| #11722180 | 2 |
| #11722179 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592727 | 3 |