Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
292 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×D4×H(3,𝔽3) | C2 | semidirect |
| 2. #3828⋊C3 | C2 | semidirect |
| 3. #3753⋊C3 | C2 | semidirect |
| 4. #3754⋊C3 | C2 | semidirect |
| 5. #3748⋊C3 | C2 | semidirect |
| 6. #64141 | C3 | semidirect |
| 13. C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 15. #634⋊C3 | C22 | semidirect |
| 16. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 18. C2×C32×D4 | D3 | semidirect |
| 19. C2×C32×D4 | C2×C3 | semidirect |
| 20. #3828 | C2×C3 | semidirect |
| 22. #3754 | C2×C3 | semidirect |
| 23. #3753 | C2×C3 | semidirect |
| 24. #3748 | C2×C3 | semidirect |
| 51. C4⋊(C3⋊D3) | C22×C3 | semidirect |
| 53. #634 | C22×C3 | semidirect |
| 58. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 100. H(3,𝔽3) | AGL(1,ℤ/8) | semidirect |
| 144. C2×D4 | (C3⋊D3)⋊C3 | semidirect |
| 175. C32 | #932 | semidirect |
| 176. C32 | C3×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×H(3,𝔽3) | 2 |
| #3828⋊C3 | 2 |
| #3753⋊C3 | 2 |
| #3754⋊C3 | 2 |
| #3748⋊C3 | 2 |
| #64141 | 3 |
| C3×#932 | 3 |