Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 278 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. #41×H(3,𝔽3) | C2 | semidirect |
| 2. C2×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. #3755⋊C3 | C2 | semidirect |
| 4. #3753⋊C3 | C2 | semidirect |
| 5. #3748⋊C3 | C2 | semidirect |
| 6. #64158 | C3 | semidirect |
| 9. Q8×H(3,𝔽3) | C22 | semidirect |
| 11. D4×H(3,𝔽3) | C22 | semidirect |
| 16. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 18. C32×#41 | D3 | semidirect |
| 19. C32×#41 | C2×C3 | semidirect |
| 20. C2×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 22. #3755 | C2×C3 | semidirect |
| 23. #3753 | C2×C3 | semidirect |
| 24. #3748 | C2×C3 | semidirect |
| 41. C32×Q8 | C2×D3 | semidirect |
| 42. C32×Q8 | C22×C3 | semidirect |
| 47. C32×D4 | C2×D3 | semidirect |
| 48. C32×D4 | C22×C3 | semidirect |
| 59. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 101. H(3,𝔽3) | AGL(1,ℤ/8) | semidirect |
| 145. #41 | (C3⋊D3)⋊C3 | semidirect |
| 177. C32 | #949 | semidirect |
| 178. C32 | C3×AGL(1,ℤ/8) | semidirect |
| 180. Q8 | C2×(C3⋊D3)⋊C3 | semidirect |
| 184. D4 | C2×(C3⋊D3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×H(3,𝔽3) | 2 |
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| #3755⋊C3 | 2 |
| #3753⋊C3 | 2 |
| #3748⋊C3 | 2 |
| #64158 | 3 |
| C3×#949 | 3 |