Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
494 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11724493 | C2 | semidirect |
| 2. #11724491 | C2 | semidirect |
| 3. C32×#131⋊C3 | C2 | semidirect |
| 4. #10596222 | C3 | semidirect |
| 11. #64366 | C2×C3 | semidirect |
| 14. C32×#131 | C2×C3 | semidirect |
| 20. C3×#131⋊C3 | D3 | semidirect |
| 55. C3×#131 | C3×D3 | semidirect |
| 61. #131⋊C3 | C3⋊D3 | semidirect |
| 127. #131 | C3×C3⋊D3 | semidirect |
| 189. C32 | #577⋊C3 | semidirect |
| 224. C3 | #5751⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724493 | 2 |
| #11724491 | 2 |
| C32×#131⋊C3 | 2 |
| #10596222 | 3 |
| #5751⋊C3 | 3 |
| C3×#3744 | 4 |