Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
152 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 52 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×C9×M16 | C2 | semidirect |
| 3. C3×C4×Dic9 | C2 | semidirect |
| 5. #63384 | C3 | direct (N × H) |
| 9. C3×D36 | C4 | semidirect |
| 11. C3×Dic18 | C4 | semidirect |
| 18. C9×M16 | C2×C3 | semidirect |
| 19. C4×Dic9 | C2×C3 | semidirect |
| 39. D36 | C3×C4 | semidirect |
| 41. Dic18 | C3×C4 | semidirect |
| 50. C3×M16 | D9 | semidirect |
| 70. C3×C9 | #104 | semidirect |
| 96. M16 | C3×D9 | semidirect |
| 115. C9 | C3×#104 | semidirect |
| 138. C3 | #63384 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3697 | 2 |
| C3×C9×M16 | 2 |
| C3×C4×Dic9 | 2 |
| C3×#825 | 3 |
| #63384 | 3 |