Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
258 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×C3×D4×C9 | C2 | semidirect |
| 2. C3×#3697 | C2 | semidirect |
| 3. C3×#3673 | C2 | semidirect |
| 4. C3×#3672 | C2 | semidirect |
| 5. C3×#3667 | C2 | semidirect |
| 7. #63495 | C3 | direct (N × H) |
| 13. C3×D36 | C22 | semidirect |
| 15. C3×Dic18 | C22 | semidirect |
| 16. C3×C9⋊C8 | C22 | semidirect |
| 23. C2×D4×C9 | C2×C3 | semidirect |
| 24. #3697 | C2×C3 | semidirect |
| 25. #3673 | C2×C3 | semidirect |
| 26. #3672 | C2×C3 | semidirect |
| 27. #3667 | C2×C3 | semidirect |
| 55. D36 | C22×C3 | semidirect |
| 57. Dic18 | C22×C3 | semidirect |
| 58. C9⋊C8 | C22×C3 | semidirect |
| 65. C2×C3×D4 | D9 | semidirect |
| 94. C3×C9 | AGL(1,ℤ/8) | semidirect |
| 129. C2×D4 | C3×D9 | semidirect |
| 154. C9 | C3×AGL(1,ℤ/8) | semidirect |
| 183. C3 | #63495 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C3×#3697 | 2 |
| C3×#3673 | 2 |
| C3×#3672 | 2 |
| C3×#3667 | 2 |
| C3×#932 | 3 |
| #63495 | 3 |