Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
516 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×D3×C8×C9 | C2 | semidirect |
| 3. #11720906 | C2 | semidirect |
| 4. #11720539 | C2 | semidirect |
| 5. C3×#63380 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. #11720277 | C2 | semidirect |
| 16. #88641 | C4 | semidirect |
| 35. #63380 | D3 | semidirect |
| 106. C2×D3×C8 | D9 | semidirect |
| 232. C3×C9 | #416 | semidirect |
| 333. C9 | #4772 | semidirect |
| 378. C3 | #10588794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88641 | 2 |
| C2×D3×C8×C9 | 2 |
| #11720906 | 2 |
| #11720539 | 2 |
| C3×#63380 | 2 |
| #11720283 | 2 |
| #11720277 | 2 |
| #10590954 | 3 |
| #10588794 | 3 |