Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1680 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1680 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. C2×C33×M16 | C2 | semidirect |
| 3. #11723965 | C2 | semidirect |
| 4. C2×#88851 | C2 | semidirect |
| 5. #11722191 | C2 | semidirect |
| 6. #11722188 | C2 | semidirect |
| 7. #11722186 | C2 | semidirect |
| 22. C2×C32×M16 | D3 | semidirect |
| 44. C33×C8 | D4 | semidirect |
| 72. C2×C3×M16 | C3⋊D3 | semidirect |
| 94. C32×C8 | #67 | semidirect |
| 128. C2×M16 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #468 | semidirect |
| 150. C3×C8 | #638 | semidirect |
| 182. C32 | #5134 | semidirect |
| 198. C8 | #6312 | semidirect |
| 217. C3 | #10592833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| #11723971 | 2 |
| #11723965 | 2 |
| C2×#88851 | 2 |
| #11722191 | 2 |
| #11722188 | 2 |
| #11722186 | 2 |
| #10592833 | 3 |