Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
621 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 621 conjugacy classes of subgroups — too many to draw. Only its 114 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. #88655 | C2 | semidirect |
| 4. #88654 | C2 | semidirect |
| 5. #88650 | C2 | semidirect |
| 7. C2×((C3⋊D3)⋊C3)⋊C2 | C22 | semidirect |
| 8. Q8×H(3,𝔽3) | C22 | semidirect |
| 9. C4⋊#272 | C22 | semidirect |
| 10. C4×#272 | C22 | semidirect |
| 11. C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 12. C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 13. #6200 | C22 | semidirect |
| 14. #6198 | C22 | semidirect |
| 15. #6196 | C22 | semidirect |
| 16. #3832 | D3 | semidirect |
| 34. C32×Q8 | C2×D3 | semidirect |
| 35. C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 36. C4×C3⋊D3 | C2×D3 | semidirect |
| 75. H(3,𝔽3) | H(5,𝔽2) | semidirect |
| 129. C32 | #1009 | semidirect |
| 132. 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 |
| #88655 | 2 |
| #88654 | 2 |
| #88650 | 2 |
| #64320 | 3 |