Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
960 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 204 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 |
|---|---|---|
| 2. C22×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 3. C2×#6199 | C2 | direct (N × H) |
| 6. C22×#272 | C4 | semidirect |
| 8. C2×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 9. #6199 | C22 | direct (N × H) |
| 12. C22×C3⋊Dic3 | D3 | semidirect |
| 15. C22×H(3,𝔽3) | C2×C4 | semidirect |
| 17. C2×#272 | C2×C4 | semidirect |
| 19. (C3⋊Dic3)⋊C3 | C23 | semidirect |
| 28. C2×C3⋊Dic3 | C2×D3 | semidirect |
| 31. C2×H(3,𝔽3) | C22×C4 | semidirect |
| 33. #272 | C22×C4 | semidirect |
| 44. C22×C32 | C4×D3 | semidirect |
| 50. C3⋊Dic3 | C22×D3 | semidirect |
| 53. H(3,𝔽3) | C23×C4 | semidirect |
| 70. C2×C32 | C2×C4×D3 | semidirect |
| 93. C32 | C22×C4×D3 | semidirect |
| 110. C22 | #6199 | direct (N × H) |
| 117. C2 | C2×#6199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#272 | 2 |
| C22×(C3⋊Dic3)⋊C3 | 2 |
| C2×#6199 | 2 |
| C22×D3×Dic3 | 3 |