Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
224 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 96 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×#3667 | C2 | semidirect |
| 4. C3×#3663 | C2 | semidirect |
| 5. C3×C8×D9 | C2 | semidirect |
| 7. M16×D9 | C3 | direct (N × H) |
| 15. C3×C8×C9 | C22 | semidirect |
| 16. C3×C9⋊C8 | C22 | semidirect |
| 24. C9×M16 | C2×C3 | semidirect |
| 25. #3667 | C2×C3 | semidirect |
| 26. #3663 | C2×C3 | semidirect |
| 27. C8×D9 | C2×C3 | semidirect |
| 56. C8×C9 | C22×C3 | semidirect |
| 57. C9⋊C8 | C22×C3 | semidirect |
| 61. C3×D9 | M16 | direct (N × H) |
| 67. C3×M16 | D9 | direct (N × H) |
| 93. C3×C9 | C2×M16 | semidirect |
| 111. C3×C8 | C2×D9 | semidirect |
| 123. D9 | C3×M16 | direct (N × H) |
| 127. M16 | C3×D9 | direct (N × H) |
| 150. C9 | C2×C3×M16 | semidirect |
| 159. C8 | C2×C3×D9 | semidirect |
| 179. C3 | M16×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D9 | 2 |
| C3×C9×M16 | 2 |
| C3×#3667 | 2 |
| C3×#3663 | 2 |
| C3×C8×D9 | 2 |
| C3×D3×M16 | 3 |
| M16×D9 | 3 |