Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
355 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 80 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. C2×((C3⋊D3)⋊C3)⋊C4 | C2 | semidirect |
| 3. C4⋊#1084 | C2 | semidirect |
| 4. C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. #88450 | C2 | semidirect |
| 13. C4⋊((C3⋊D3)⋊C3) | C4 | semidirect |
| 19. C4×C3⋊Dic3 | D3 | semidirect |
| 29. C2×(C3⋊D3)⋊C3 | C2×C4 | semidirect |
| 30. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 33. (C3⋊Dic3)⋊C3 | D4 | semidirect |
| 44. C4⋊(C3⋊D3) | Dic3 | semidirect |
| 78. C2×C3⋊D3 | C2×Dic3 | semidirect |
| 83. C32×C4 | C4×D3 | semidirect |
| 84. C32×C4 | C2×Dic3 | semidirect |
| 86. C3⋊Dic3 | D12 | semidirect |
| 93. H(3,𝔽3) | C4×D4 | semidirect |
| 161. C32 | C4×D12 | semidirect |
| 162. C32 | D4×Dic3 | semidirect |
| 192. C4 | ((C3⋊D3)⋊C3)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| C2×((C3⋊D3)⋊C3)⋊C4 | 2 |
| C4⋊#1084 | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| #88450 | 2 |
| #63898 | 3 |
| #63894 | 3 |