Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
420 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 131 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. C3×C9×#135 | C2 | semidirect |
| 2. #11721773 | C2 | semidirect |
| 3. #11720568 | C2 | semidirect |
| 4. #11720567 | C2 | semidirect |
| 5. #11720564 | C2 | semidirect |
| 6. #11720563 | C2 | semidirect |
| 7. C2×C3⋊(C9⋊C16) | C2 | semidirect |
| 28. C9×#135 | D3 | semidirect |
| 77. C3×#135 | D9 | semidirect |
| 155. #135 | C3⋊D9 | semidirect |
| 161. C3×C9 | #508 | semidirect |
| 218. C9 | #5194 | semidirect |
| 245. C3 | #10588874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#135 | 2 |
| #11721773 | 2 |
| #11720568 | 2 |
| #11720567 | 2 |
| #11720564 | 2 |
| #11720563 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| #10592893 | 3 |
| #10588874 | 3 |