Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 101 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×#88524 | C2 | semidirect |
| 2. C2×C3×#3664 | C2 | semidirect |
| 3. #11720952 | C2 | semidirect |
| 4. #11720948 | C2 | semidirect |
| 5. C2×#88418 | C2 | semidirect |
| 7. C8×C9×Dic3 | C2 | semidirect |
| 33. C2×#3664 | D3 | semidirect |
| 110. C8×Dic3 | D9 | semidirect |
| 219. C3×C9 | #495 | semidirect |
| 312. C9 | #5168 | semidirect |
| 351. C3 | #10588378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| C2×C3×#3664 | 2 |
| #11720952 | 2 |
| #11720948 | 2 |
| C2×#88418 | 2 |
| C2×#88417 | 2 |
| C8×C9×Dic3 | 2 |
| #10590862 | 3 |
| #10588378 | 3 |