Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1148 conjugacy classes of subgroups; only the 347 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 347 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×Q16 | C2 | semidirect |
| 3. #11722199 | C2 | semidirect |
| 4. #11722198 | C2 | semidirect |
| 5. #11722182 | C2 | semidirect |
| 16. C2×C32×Q16 | D3 | semidirect |
| 47. C2×C3×Q16 | C3⋊D3 | semidirect |
| 82. C2×Q16 | C3⋊(C3⋊D3) | semidirect |
| 86. C33 | #510 | semidirect |
| 115. C32 | #5179 | semidirect |
| 135. C3 | #10592878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| #11723945 | 2 |
| #11722199 | 2 |
| #11722198 | 2 |
| #11722182 | 2 |
| #10592878 | 3 |