Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
258 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 87 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. #3748⋊C3 | C2 | semidirect |
| 4. #3743⋊C3 | C2 | semidirect |
| 5. C8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 6. M16×C3⋊D3 | C3 | semidirect |
| 15. C8×H(3,𝔽3) | C22 | semidirect |
| 16. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 20. C32×M16 | D3 | semidirect |
| 21. C32×M16 | C2×C3 | semidirect |
| 22. #3748 | C2×C3 | semidirect |
| 23. #3743 | C2×C3 | semidirect |
| 24. C8×C3⋊D3 | C2×C3 | semidirect |
| 55. C32×C8 | C2×D3 | semidirect |
| 56. C32×C8 | C22×C3 | semidirect |
| 57. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 62. (C3⋊D3)⋊C3 | M16 | direct (N × H) |
| 99. H(3,𝔽3) | C2×M16 | semidirect |
| 136. C3⋊D3 | C3×M16 | semidirect |
| 142. M16 | (C3⋊D3)⋊C3 | direct (N × H) |
| 172. C32 | D3×M16 | semidirect |
| 173. C32 | C2×C3×M16 | semidirect |
| 182. C8 | C2×(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 |
| M16×H(3,𝔽3) | 2 |
| #3748⋊C3 | 2 |
| #3743⋊C3 | 2 |
| C8×(C3⋊D3)⋊C3 | 2 |
| M16×C3⋊D3 | 3 |
| C3×D3×M16 | 3 |