Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
432 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 162 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. C32×D3×Q8 | C2 | semidirect |
| 3. C33×Q16 | C2 | semidirect |
| 4. C32×#216 | C2 | semidirect |
| 5. C32×#215 | C2 | semidirect |
| 6. C32×#204 | C2 | semidirect |
| 7. C32×ΓL(1,𝔽25) | C2 | semidirect |
| 9. C3×#918 | C3 | direct (N × H) |
| 24. C3×D3×Q8 | C2×C3 | semidirect |
| 27. C32×Q16 | D3 | semidirect |
| 28. C32×Q16 | C2×C3 | semidirect |
| 32. C3×#216 | C2×C3 | semidirect |
| 33. C3×#215 | C2×C3 | semidirect |
| 34. C3×#204 | C2×C3 | semidirect |
| 35. C3×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 44. #918 | C32 | direct (N × H) |
| 76. D3×Q8 | C2×C32 | semidirect |
| 79. C3×Q16 | C3×D3 | semidirect |
| 80. C3×Q16 | C2×C32 | semidirect |
| 84. #216 | C2×C32 | semidirect |
| 85. #215 | C2×C32 | semidirect |
| 86. #204 | C2×C32 | semidirect |
| 87. ΓL(1,𝔽25) | C2×C32 | semidirect |
| 106. C33 | #137 | semidirect |
| 142. Q16 | C32×D3 | semidirect |
| 164. C32 | #918 | direct (N × H) |
| 165. C32 | C3×#137 | semidirect |
| 192. C3 | C3×#918 | direct (N × H) |
| 193. C3 | C32×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#239 | 2 |
| C32×D3×Q8 | 2 |
| C33×Q16 | 2 |
| C32×#216 | 2 |
| C32×#215 | 2 |
| C32×#204 | 2 |
| C32×ΓL(1,𝔽25) | 2 |
| C32×#137 | 3 |
| C3×#918 | 3 |