Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1512 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 349 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×C33×D8 | C2 | semidirect |
| 2. #11723973 | C2 | semidirect |
| 3. #11723942 | C2 | semidirect |
| 4. #11722203 | C2 | semidirect |
| 5. #11722189 | C2 | semidirect |
| 18. C2×C32×D8 | D3 | semidirect |
| 54. C2×C3×D8 | C3⋊D3 | semidirect |
| 95. C2×D8 | C3⋊(C3⋊D3) | semidirect |
| 99. C33 | #472 | semidirect |
| 134. C32 | #5160 | semidirect |
| 158. C3 | #10592859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| #11723973 | 2 |
| #11723942 | 2 |
| #11722203 | 2 |
| #11722189 | 2 |
| #10592859 | 3 |