Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
444 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 1. C32×#239 | C2 | semidirect |
| 2. C33×Q16 | C2 | semidirect |
| 3. C32×#215 | C2 | semidirect |
| 4. C32×D24 | C2 | semidirect |
| 5. C32×D3×C8 | C2 | semidirect |
| 7. C3×#919 | C3 | direct (N × H) |
| 16. C3×#239 | C2×C3 | semidirect |
| 18. C32×Q16 | D3 | semidirect |
| 19. C32×Q16 | C2×C3 | semidirect |
| 23. C3×#215 | C2×C3 | semidirect |
| 24. C3×D24 | C2×C3 | semidirect |
| 25. C3×D3×C8 | C2×C3 | semidirect |
| 32. #919 | C32 | direct (N × H) |
| 53. #239 | C2×C32 | semidirect |
| 55. C3×Q16 | C3×D3 | semidirect |
| 56. C3×Q16 | C2×C32 | semidirect |
| 60. #215 | C2×C32 | semidirect |
| 61. D24 | C2×C32 | semidirect |
| 62. D3×C8 | C2×C32 | semidirect |
| 76. C33 | #135 | semidirect |
| 101. Q16 | C32×D3 | semidirect |
| 118. C32 | #919 | direct (N × H) |
| 119. C32 | C3×#135 | semidirect |
| 140. C3 | C3×#919 | direct (N × H) |
| 141. C3 | C32×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#239 | 2 |
| C33×Q16 | 2 |
| C32×#215 | 2 |
| C32×D24 | 2 |
| C32×D3×C8 | 2 |
| C32×#135 | 3 |
| C3×#919 | 3 |