Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
348 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 109 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⋊C4×H(3,𝔽3) | C2 | semidirect |
| 4. C4⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 5. #3750⋊C3 | C2 | semidirect |
| 6. C4⋊C4×C3⋊D3 | C3 | semidirect |
| 14. C4×(C3⋊D3)⋊C3 | C4 | semidirect |
| 20. C32×C4⋊C4 | D3 | semidirect |
| 21. C32×C4⋊C4 | C2×C3 | semidirect |
| 22. C4⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 23. #3750 | C2×C3 | semidirect |
| 31. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 33. (C3⋊Dic3)⋊C3 | C2×C4 | semidirect |
| 48. C4×C3⋊D3 | C3×C4 | semidirect |
| 56. (C3⋊D3)⋊C3 | C4⋊C4 | direct (N × H) |
| 86. C32×C4 | C4×D3 | semidirect |
| 87. C32×C4 | C2×C3×C4 | semidirect |
| 89. C3⋊Dic3 | C2×C3×C4 | semidirect |
| 93. H(3,𝔽3) | C2×C4⋊C4 | semidirect |
| 126. C3⋊D3 | C3×C4⋊C4 | semidirect |
| 132. C4⋊C4 | (C3⋊D3)⋊C3 | direct (N × H) |
| 161. C32 | D3×C4⋊C4 | semidirect |
| 162. C32 | C2×C3×C4⋊C4 | semidirect |
| 192. C4 | C4×(C3⋊D3)⋊C3 | 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 |
| C4⋊C4×H(3,𝔽3) | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| #3750⋊C3 | 2 |
| C4⋊C4×C3⋊D3 | 3 |
| C3×D3×C4⋊C4 | 3 |