Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
418 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C9×#817 | C2 | semidirect |
| 4. C3×#63377 | C2 | semidirect |
| 5. #11720263 | C2 | semidirect |
| 11. C8×C3⋊D9 | C4 | semidirect |
| 25. #63377 | D3 | semidirect |
| 74. #817 | D9 | semidirect |
| 153. C3×C9 | #427 | semidirect |
| 220. C9 | #4860 | semidirect |
| 248. C3 | #10588540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D9 | 2 |
| #11720922 | 2 |
| C9×#817 | 2 |
| C3×#63377 | 2 |
| #11720263 | 2 |
| #10590712 | 3 |
| #10588540 | 3 |