Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
383 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 121 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. #3757⋊C3 | C2 | semidirect |
| 4. C4⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 5. C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 6. D4×C3⋊Dic3 | C3 | semidirect |
| 9. D4×H(3,𝔽3) | C4 | semidirect |
| 18. C22×C3⋊Dic3 | C2×C3 | semidirect |
| 20. #3757 | C2×C3 | semidirect |
| 21. C4⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 22. C4×C3⋊Dic3 | C2×C3 | semidirect |
| 28. C22×H(3,𝔽3) | C2×C4 | semidirect |
| 30. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 33. (C3⋊Dic3)⋊C3 | D4 | direct (N × H) |
| 41. C32×D4 | Dic3 | semidirect |
| 42. C32×D4 | C3×C4 | semidirect |
| 82. C22×C32 | C2×Dic3 | semidirect |
| 83. C22×C32 | C2×C3×C4 | semidirect |
| 87. C32×C4 | C2×Dic3 | semidirect |
| 88. C32×C4 | C2×C3×C4 | semidirect |
| 91. C3⋊Dic3 | C3×D4 | semidirect |
| 96. H(3,𝔽3) | C4×D4 | semidirect |
| 168. C32 | D4×Dic3 | semidirect |
| 169. C32 | C3×C4×D4 | semidirect |
| 171. D4 | (C3⋊Dic3)⋊C3 | direct (N × H) |
| 195. C22 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 200. C4 | C2×(C3⋊Dic3)⋊C3 | 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 |
| C22×(C3⋊Dic3)⋊C3 | 2 |
| #3757⋊C3 | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| D4×C3⋊Dic3 | 3 |
| C3×D4×Dic3 | 3 |