Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
624 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 128 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. C2×C32×C3⋊C8 | C2 | semidirect |
| 4. #88797 | C2 | direct (N × H) |
| 13. C3×#634 | C22 | semidirect |
| 14. C32×C3⋊C8 | C22 | semidirect |
| 18. C2×#634 | D3 | semidirect |
| 22. C2×C3×C3⋊C8 | D3 | semidirect |
| 46. #634 | C2×D3 | semidirect |
| 51. C3×C3⋊C8 | C2×D3 | semidirect |
| 52. C2×C33 | SD16 | semidirect |
| 62. C2×C3⋊C8 | C3⋊D3 | semidirect |
| 82. C33 | C2×SD16 | semidirect |
| 102. C3⋊C8 | C2×C3⋊D3 | semidirect |
| 105. C2×C32 | #204 | semidirect |
| 106. C2×C32 | #215 | semidirect |
| 134. C32 | C2×#204 | semidirect |
| 135. C32 | C2×#215 | semidirect |
| 146. C2×C3 | #3717 | semidirect |
| 147. C2×C3 | #3744 | semidirect |
| 160. C3 | C2×#3717 | semidirect |
| 161. C3 | C2×#3744 | semidirect |
| 163. C2 | #88797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C2×C3×#634 | 2 |
| C2×C32×C3⋊C8 | 2 |
| #88797 | 2 |
| C2×#3744 | 3 |
| C2×#3717 | 3 |