Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
432 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. #88447 | C2 | semidirect |
| 11. C4×#272 | C4 | semidirect |
| 14. #6199 | C4 | direct (N × H) |
| 20. C4×C3⋊Dic3 | D3 | semidirect |
| 21. C4×C3⋊Dic3 | D3 | semidirect |
| 29. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 30. #1084 | C2×C4 | semidirect |
| 31. (C3⋊Dic3)⋊C3 | C2×C4 | semidirect |
| 32. (C3⋊Dic3)⋊C3 | C2×C4 | semidirect |
| 56. #272 | C42 | semidirect |
| 83. C32×C4 | C4×D3 | semidirect |
| 84. C32×C4 | C4×D3 | semidirect |
| 85. C3⋊Dic3 | C4×D3 | semidirect |
| 86. C3⋊Dic3 | C4×D3 | semidirect |
| 93. H(3,𝔽3) | C2×C42 | semidirect |
| 160. C32 | C42×D3 | semidirect |
| 161. C32 | C42×D3 | semidirect |
| 187. C4 | #6199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#272 | 2 |
| C2×#6199 | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| #88447 | 2 |
| C4×D3×Dic3 | 3 |