Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11721840 | C2 | semidirect |
| 2. C2×C9×#213 | C2 | semidirect |
| 3. C2×C3×#3672 | C2 | semidirect |
| 4. #11720967 | C2 | semidirect |
| 5. C2×#88422 | C2 | semidirect |
| 6. C2×#88416 | C2 | semidirect |
| 7. #11720275 | C2 | semidirect |
| 35. C2×#3672 | D3 | semidirect |
| 53. C9×C3⋊C8 | D4 | semidirect |
| 54. C3×C9⋊C8 | D4 | semidirect |
| 108. C2×#213 | D9 | semidirect |
| 155. C9⋊C8 | #67 | semidirect |
| 229. C3×C9 | #496 | semidirect |
| 272. C3⋊C8 | #611 | semidirect |
| 332. C9 | #5176 | semidirect |
| 376. C3 | #10588834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721840 | 2 |
| C2×C9×#213 | 2 |
| C2×C3×#3672 | 2 |
| #11720967 | 2 |
| C2×#88422 | 2 |
| C2×#88416 | 2 |
| #11720275 | 2 |
| #10591475 | 3 |
| #10588834 | 3 |