Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 91 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×#88532 | C2 | semidirect |
| 2. C9×#930 | C2 | semidirect |
| 3. C3×#63492 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 6. #11720266 | C2 | semidirect |
| 7. #11720265 | C2 | semidirect |
| 32. #63492 | D3 | semidirect |
| 54. C3⋊(C9⋊C8) | D4 | semidirect |
| 107. #930 | D9 | semidirect |
| 239. C3×C9 | #469 | semidirect |
| 349. C9 | #5039 | semidirect |
| 399. C3 | #10588722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88532 | 2 |
| C9×#930 | 2 |
| C3×#63492 | 2 |
| C2×#88421 | 2 |
| #11720294 | 2 |
| #11720266 | 2 |
| #11720265 | 2 |
| #10591167 | 3 |
| #10588722 | 3 |