Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
952 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 263 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. C33×#41 | C2 | semidirect |
| 2. C2×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 3. #88862 | C2 | semidirect |
| 4. #88860 | C2 | semidirect |
| 5. #88855 | C2 | semidirect |
| 8. C33×Q8 | C22 | semidirect |
| 10. C33×D4 | C22 | semidirect |
| 15. C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 16. C32×#41 | D3 | semidirect |
| 30. C32×Q8 | C2×D3 | semidirect |
| 32. C32×D4 | C2×D3 | semidirect |
| 42. C3×#41 | C3⋊D3 | semidirect |
| 55. C33 | AGL(1,ℤ/8) | semidirect |
| 57. C3×Q8 | C2×C3⋊D3 | semidirect |
| 59. C3×D4 | C2×C3⋊D3 | semidirect |
| 69. #41 | C3⋊(C3⋊D3) | semidirect |
| 81. C32 | #949 | semidirect |
| 83. Q8 | C2×C3⋊(C3⋊D3) | semidirect |
| 87. D4 | C2×C3⋊(C3⋊D3) | semidirect |
| 102. C3 | #64158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#41 | 2 |
| C2×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #88862 | 2 |
| #88860 | 2 |
| #88855 | 2 |
| #64158 | 3 |