Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
368 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11720906 | C2 | semidirect |
| 3. #11720576 | C2 | semidirect |
| 4. C3×#63392 | C2 | semidirect |
| 5. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 6. #11720264 | C2 | semidirect |
| 7. #11720263 | C2 | semidirect |
| 32. #63392 | D3 | semidirect |
| 210. C3×C9 | #482 | semidirect |
| 305. C9 | #4779 | semidirect |
| 348. C3 | #10588715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#938 | 2 |
| #11720906 | 2 |
| #11720576 | 2 |
| C3×#63392 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #11720264 | 2 |
| #11720263 | 2 |
| #10591422 | 3 |
| #10588715 | 3 |