Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
488 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 234 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. C33×M16 | C2 | semidirect |
| 3. C32×#208 | C2 | semidirect |
| 4. C32×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C32×D3×C8 | C2 | semidirect |
| 7. C3×D3×M16 | C3 | direct (N × H) |
| 15. C33×C8 | C22 | semidirect |
| 16. C32×C3⋊C8 | C22 | semidirect |
| 22. C32×M16 | D3 | direct (N × H) |
| 23. C32×M16 | C2×C3 | semidirect |
| 25. C3×#208 | C2×C3 | semidirect |
| 26. C3×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 27. C3×D3×C8 | C2×C3 | semidirect |
| 37. D3×M16 | C32 | direct (N × H) |
| 55. C32×C8 | C2×D3 | semidirect |
| 56. C32×C8 | C22×C3 | semidirect |
| 57. C3×C3⋊C8 | C22×C3 | semidirect |
| 61. C32×D3 | M16 | direct (N × H) |
| 67. C3×M16 | C3×D3 | direct (N × H) |
| 68. C3×M16 | C2×C32 | semidirect |
| 70. #208 | C2×C32 | semidirect |
| 71. ΓL(1,𝔽25) | C2×C32 | semidirect |
| 72. D3×C8 | C2×C32 | semidirect |
| 93. C33 | C2×M16 | semidirect |
| 111. C3×C8 | C2×C3×D3 | semidirect |
| 112. C3×C8 | C22×C32 | semidirect |
| 113. C3⋊C8 | C22×C32 | semidirect |
| 123. C3×D3 | C3×M16 | direct (N × H) |
| 127. M16 | C32×D3 | direct (N × H) |
| 149. C32 | D3×M16 | direct (N × H) |
| 150. C32 | C2×C3×M16 | semidirect |
| 159. C8 | C2×C32×D3 | semidirect |
| 169. D3 | C32×M16 | direct (N × H) |
| 179. C3 | C3×D3×M16 | direct (N × H) |
| 180. C3 | C2×C32×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D3 | 2 |
| C33×M16 | 2 |
| C32×#208 | 2 |
| C32×ΓL(1,𝔽25) | 2 |
| C32×D3×C8 | 2 |
| C2×C32×M16 | 3 |
| C3×D3×M16 | 3 |