Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
952 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 211 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. Q8×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C33×SD16 | C2 | semidirect |
| 4. #88862 | C2 | semidirect |
| 5. #88861 | C2 | semidirect |
| 6. #88851 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 10. C33×Q8 | C22 | semidirect |
| 17. #6308 | C22 | semidirect |
| 18. C33×C8 | C22 | semidirect |
| 19. C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 22. C32×SD16 | D3 | semidirect |
| 37. C32×Q8 | C2×D3 | semidirect |
| 45. C32×C8 | C2×D3 | semidirect |
| 50. C3⋊(C3⋊D3) | SD16 | direct (N × H) |
| 53. C3×SD16 | C3⋊D3 | semidirect |
| 67. C33 | C2×SD16 | semidirect |
| 69. C3×Q8 | C2×C3⋊D3 | semidirect |
| 77. C3×C8 | C2×C3⋊D3 | semidirect |
| 88. SD16 | C3⋊(C3⋊D3) | direct (N × H) |
| 98. C32 | D3×SD16 | semidirect |
| 102. Q8 | C2×C3⋊(C3⋊D3) | semidirect |
| 109. C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 122. C3 | SD16×C3⋊D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊(C3⋊D3) | 2 |
| D4×C3⋊(C3⋊D3) | 2 |
| C33×SD16 | 2 |
| #88862 | 2 |
| #88861 | 2 |
| #88851 | 2 |
| C8×C3⋊(C3⋊D3) | 2 |
| SD16×C3⋊D3 | 3 |