Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
614 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 118 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. #88748 | C2 | semidirect |
| 2. #88722 | C2 | semidirect |
| 3. Q8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. #88654 | C2 | semidirect |
| 5. C4×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 6. #88652 | C2 | semidirect |
| 7. #88649 | C2 | semidirect |
| 11. Q8×H(3,𝔽3) | C22 | semidirect |
| 12. C4⋊#272 | C22 | semidirect |
| 13. C4×#272 | C22 | semidirect |
| 14. C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 16. C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 17. #634⋊C3 | C22 | semidirect |
| 18. #6200 | C22 | semidirect |
| 19. #6199 | C22 | semidirect |
| 21. ((C3⋊D3)⋊C3)⋊C4 | C22 | semidirect |
| 22. #3832 | D3 | semidirect |
| 23. Q8×C3⋊D3 | D3 | semidirect |
| 51. C32×Q8 | C2×D3 | semidirect |
| 52. C32×Q8 | C2×D3 | semidirect |
| 53. C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 55. C4×C3⋊D3 | C2×D3 | semidirect |
| 56. #634 | C2×D3 | semidirect |
| 78. (C3⋊D3)⋊C3 | #41 | semidirect |
| 121. H(3,𝔽3) | C2×#41 | semidirect |
| 165. C3⋊D3 | #239 | semidirect |
| 206. C32 | C2×#239 | semidirect |
| 207. C32 | D3×#41 | semidirect |
| 210. Q8 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88748 | 2 |
| #88722 | 2 |
| Q8×(C3⋊D3)⋊C3 | 2 |
| #88654 | 2 |
| C4×((C3⋊D3)⋊C3)⋊C2 | 2 |
| #88652 | 2 |
| #88649 | 2 |
| #64319 | 3 |
| D3×#239 | 3 |