Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
624 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 154 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. C2×C3×#634 | C2 | semidirect |
| 3. C3×#3754 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. C2×#3754 | C3 | direct (N × H) |
| 13. C3×#634 | C22 | semidirect |
| 14. C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 18. C2×#634 | C2×C3 | semidirect |
| 20. #3754 | C2×C3 | direct (N × H) |
| 21. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 46. #634 | C22×C3 | semidirect |
| 50. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 53. C2×C33 | SD16 | semidirect |
| 82. C33 | C2×SD16 | semidirect |
| 108. C2×C32 | #214 | semidirect |
| 109. C2×C32 | C3×SD16 | semidirect |
| 134. C32 | C2×#214 | semidirect |
| 135. C32 | C2×C3×SD16 | semidirect |
| 149. C2×C3 | C3×#214 | semidirect |
| 150. C2×C3 | #3754 | direct (N × H) |
| 160. C3 | C2×C3×#214 | semidirect |
| 161. C3 | C2×#3754 | direct (N × H) |
| 163. C2 | C3×#3754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D4 | 2 |
| C2×C3×#634 | 2 |
| C3×#3754 | 2 |
| C2×C3×C3⋊(C3⋊C8) | 2 |
| C2×#3754 | 3 |
| C2×C3×#214 | 3 |