Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
532 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 226 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. C3×#3748 | C2 | semidirect |
| 3. C2×C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #64157 | C3 | direct (N × H) |
| 14. #3748 | C2×C3 | semidirect |
| 15. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 55. C33 | #131 | semidirect |
| 88. C32 | #948 | semidirect |
| 89. C32 | C3×#131 | semidirect |
| 105. C3 | C3×#948 | semidirect |
| 106. C3 | #64157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#41 | 2 |
| C3×#3748 | 2 |
| C2×C3×C3⋊(C3⋊C8) | 2 |
| #64157 | 3 |
| C3×#948 | 3 |