Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
452 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 146 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. C2×C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C3×#3743 | C2 | semidirect |
| 5. C3×C8×C3⋊D3 | C2 | semidirect |
| 6. #64116 | C3 | direct (N × H) |
| 19. C32×M16 | D3 | semidirect |
| 20. C32×M16 | C2×C3 | semidirect |
| 21. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 22. #3743 | C2×C3 | semidirect |
| 23. C8×C3⋊D3 | C2×C3 | semidirect |
| 59. C3×M16 | C3×D3 | semidirect |
| 60. C3×M16 | C3⋊D3 | semidirect |
| 80. C33 | #131 | semidirect |
| 109. M16 | C3×C3⋊D3 | semidirect |
| 126. C32 | #907 | semidirect |
| 127. C32 | C3×#131 | semidirect |
| 150. C3 | C3×#907 | semidirect |
| 151. C3 | #64116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3828 | 2 |
| C33×M16 | 2 |
| C2×C3×C3⋊(C3⋊C8) | 2 |
| C3×#3743 | 2 |
| C3×C8×C3⋊D3 | 2 |
| #64116 | 3 |
| C3×#907 | 3 |