Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 2. C3×#63511 | C2 | semidirect |
| 3. #11720967 | C2 | semidirect |
| 4. #11720887 | C2 | semidirect |
| 5. #11720585 | C2 | semidirect |
| 6. #11720300 | C2 | semidirect |
| 7. #11720296 | C2 | semidirect |
| 18. C2×C3×Dic18 | C22 | semidirect |
| 19. C4×C3⋊Dic9 | C22 | semidirect |
| 20. #88532 | C22 | semidirect |
| 23. C3×#3667 | C22 | semidirect |
| 36. #63511 | D3 | semidirect |
| 92. C2×Dic18 | C2×D3 | semidirect |
| 102. #3667 | C2×D3 | semidirect |
| 261. C3×C9 | #455 | semidirect |
| 375. C9 | #5202 | semidirect |
| 424. C3 | #10588921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1009 | 2 |
| C3×#63511 | 2 |
| #11720967 | 2 |
| #11720887 | 2 |
| #11720585 | 2 |
| #11720300 | 2 |
| #11720296 | 2 |
| #10591664 | 3 |
| #10588921 | 3 |