Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
560 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 560 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 |
|---|---|---|
| 1. C2×C33×Q8 | C2 | semidirect |
| 3. C3×#3755 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. C2×#3755 | C3 | direct (N × H) |
| 9. C33×Q8 | C22 | semidirect |
| 14. C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 16. C2×C32×Q8 | D3 | semidirect |
| 17. C2×C32×Q8 | C2×C3 | semidirect |
| 20. #3755 | C2×C3 | direct (N × H) |
| 21. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 38. C32×Q8 | C2×D3 | semidirect |
| 39. C32×Q8 | C22×C3 | semidirect |
| 50. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 52. C2×C33 | SD16 | semidirect |
| 56. C2×C3×Q8 | C3×D3 | semidirect |
| 57. C2×C3×Q8 | C3⋊D3 | semidirect |
| 81. C33 | C2×SD16 | semidirect |
| 88. C3×Q8 | C2×C3×D3 | semidirect |
| 89. C3×Q8 | C2×C3⋊D3 | semidirect |
| 104. C2×C32 | #215 | semidirect |
| 105. C2×C32 | C3×SD16 | semidirect |
| 110. C2×Q8 | C3×C3⋊D3 | semidirect |
| 131. C32 | C2×#215 | semidirect |
| 132. C32 | C2×C3×SD16 | semidirect |
| 135. Q8 | C2×C3×C3⋊D3 | semidirect |
| 144. C2×C3 | C3×#215 | semidirect |
| 145. C2×C3 | #3755 | direct (N × H) |
| 156. C3 | C2×C3×#215 | semidirect |
| 157. C3 | C2×#3755 | direct (N × H) |
| 159. C2 | C3×#3755 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q8 | 2 |
| C2×C3×C4⋊(C3⋊D3) | 2 |
| C3×#3755 | 2 |
| C2×C3×C3⋊(C3⋊C8) | 2 |
| C2×#3755 | 3 |
| C2×C3×#215 | 3 |