Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
237 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 83 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. M16×H(3,𝔽3) | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 4. #3743⋊C3 | C2 | semidirect |
| 5. C8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 6. #64116 | C3 | semidirect |
| 19. C32×M16 | D3 | semidirect |
| 20. C32×M16 | C2×C3 | semidirect |
| 21. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 22. #3743 | C2×C3 | semidirect |
| 23. C8×C3⋊D3 | C2×C3 | semidirect |
| 86. H(3,𝔽3) | #131 | semidirect |
| 123. M16 | (C3⋊D3)⋊C3 | semidirect |
| 145. C32 | #907 | semidirect |
| 146. C32 | C3×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3828⋊C3 | 2 |
| M16×H(3,𝔽3) | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #3743⋊C3 | 2 |
| C8×(C3⋊D3)⋊C3 | 2 |
| #64116 | 3 |
| C3×#907 | 3 |