Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 407 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. #11723985 | C2 | semidirect |
| 4. C2×#88863 | C2 | semidirect |
| 7. #11722185 | C2 | semidirect |
| 22. C2×C32×Q16 | D3 | semidirect |
| 68. C2×C3×Q16 | C3⋊D3 | semidirect |
| 118. C2×Q16 | C3⋊(C3⋊D3) | semidirect |
| 124. C33 | #497 | semidirect |
| 166. C32 | #5190 | semidirect |
| 195. C3 | #10592889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| #11723988 | 2 |
| #11723985 | 2 |
| C2×#88863 | 2 |
| C2×#88862 | 2 |
| C2×#88851 | 2 |
| #11722185 | 2 |
| #10592889 | 3 |