Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
628 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#638⋊C3 | C2 | semidirect |
| 3. C22×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. #3830⋊C3 | C2 | direct (N × H) |
| 5. C2×C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 6. C2×#634⋊C3 | C2 | semidirect |
| 7. C2×#3830 | C3 | semidirect |
| 11. D4×H(3,𝔽3) | C22 | semidirect |
| 13. #638⋊C3 | C22 | semidirect |
| 16. C2×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 17. C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 18. #634⋊C3 | C22 | semidirect |
| 20. C2×C32×D4 | D3 | semidirect |
| 21. C2×C32×D4 | C2×C3 | semidirect |
| 22. C2×#638 | C2×C3 | semidirect |
| 23. C22×C3⋊Dic3 | C2×C3 | semidirect |
| 24. #3830 | C2×C3 | semidirect |
| 25. C2×C4×C3⋊D3 | C2×C3 | semidirect |
| 26. C2×#634 | C2×C3 | semidirect |
| 49. C32×D4 | C2×D3 | semidirect |
| 50. C32×D4 | C22×C3 | semidirect |
| 54. #638 | C22×C3 | semidirect |
| 57. C2×C3⋊Dic3 | C22×C3 | semidirect |
| 58. C4×C3⋊D3 | C22×C3 | semidirect |
| 59. #634 | C22×C3 | semidirect |
| 67. C2×H(3,𝔽3) | #41 | semidirect |
| 110. H(3,𝔽3) | C2×#41 | semidirect |
| 149. C2×C32 | #237 | semidirect |
| 150. C2×C32 | C3×#41 | semidirect |
| 158. C2×D4 | (C3⋊D3)⋊C3 | semidirect |
| 190. C32 | C2×#237 | semidirect |
| 191. C32 | C2×C3×#41 | semidirect |
| 196. D4 | C2×(C3⋊D3)⋊C3 | semidirect |
| 231. C2 | #3830⋊C3 | direct (N × H) |
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 |
| C2×#638⋊C3 | 2 |
| C22×(C3⋊Dic3)⋊C3 | 2 |
| #3830⋊C3 | 2 |
| C2×C4×(C3⋊D3)⋊C3 | 2 |
| C2×#634⋊C3 | 2 |
| C2×#3830 | 3 |
| C2×C3×#237 | 3 |