Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
510 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 153 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. #11721707 | C2 | semidirect |
| 3. C3×C9×C4⋊C8 | C2 | semidirect |
| 6. #11720541 | C2 | semidirect |
| 7. #11720540 | C2 | semidirect |
| 30. C9×C4⋊C8 | D3 | semidirect |
| 86. C3×C4⋊C8 | D9 | semidirect |
| 173. C4⋊C8 | C3⋊D9 | semidirect |
| 176. C3×C9 | #478 | semidirect |
| 243. C9 | #4847 | semidirect |
| 275. C3 | #10588531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D9) | 2 |
| #11721707 | 2 |
| C3×C9×C4⋊C8 | 2 |
| #11720543 | 2 |
| #11720541 | 2 |
| #11720540 | 2 |
| #10592546 | 3 |
| #10588531 | 3 |