Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
952 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 209 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. #89080 | C2 | semidirect |
| 2. D4×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C33×SD16 | C2 | semidirect |
| 4. #88862 | C2 | semidirect |
| 5. #88860 | C2 | semidirect |
| 6. #88852 | C2 | semidirect |
| 7. #88850 | C2 | semidirect |
| 10. C33×Q8 | C22 | semidirect |
| 15. C4⋊(C3⋊(C3⋊D3)) | 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 |
| 54. C3×SD16 | C3⋊D3 | semidirect |
| 68. C33 | AGL(1,ℤ/8) | semidirect |
| 70. C3×Q8 | C2×C3⋊D3 | semidirect |
| 78. C3×C8 | C2×C3⋊D3 | semidirect |
| 88. SD16 | C3⋊(C3⋊D3) | semidirect |
| 100. C32 | #914 | semidirect |
| 102. Q8 | C2×C3⋊(C3⋊D3) | semidirect |
| 111. C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 125. C3 | #64123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89080 | 2 |
| D4×C3⋊(C3⋊D3) | 2 |
| C33×SD16 | 2 |
| #88862 | 2 |
| #88860 | 2 |
| #88852 | 2 |
| #88850 | 2 |
| #64123 | 3 |