Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
288 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 2. C2×C8×H(3,𝔽3) | C2 | semidirect |
| 3. #3745⋊C3 | C2 | direct (N × H) |
| 4. C2×#3745 | C3 | semidirect |
| 9. C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 10. C8×H(3,𝔽3) | C22 | semidirect |
| 11. C2×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 14. C2×C32×C8 | D3 | semidirect |
| 15. C2×C32×C8 | C2×C3 | semidirect |
| 16. #3745 | C2×C3 | semidirect |
| 32. C4⋊(C3⋊D3) | C22×C3 | semidirect |
| 36. C32×C8 | C2×D3 | semidirect |
| 37. C32×C8 | C22×C3 | semidirect |
| 38. C2×H(3,𝔽3) | D8 | semidirect |
| 65. H(3,𝔽3) | C2×D8 | semidirect |
| 85. C2×C32 | D24 | semidirect |
| 86. C2×C32 | C3×D8 | semidirect |
| 93. C2×C8 | (C3⋊D3)⋊C3 | semidirect |
| 113. C32 | C2×D24 | semidirect |
| 114. C32 | C2×C3×D8 | semidirect |
| 119. C8 | C2×(C3⋊D3)⋊C3 | semidirect |
| 141. C2 | #3745⋊C3 | direct (N × H) |
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×C8×H(3,𝔽3) | 2 |
| #3745⋊C3 | 2 |
| C2×#3745 | 3 |
| C2×C3×D24 | 3 |