Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
496 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 496 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×C32×Dic6 | C2 | semidirect |
| 3. C2×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #88793 | C2 | direct (N × H) |
| 13. C32×Dic6 | C22 | semidirect |
| 14. C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 18. C2×C3×Dic6 | D3 | semidirect |
| 46. C3×Dic6 | C2×D3 | semidirect |
| 50. C2×C33 | SD16 | semidirect |
| 56. C2×Dic6 | C3⋊D3 | semidirect |
| 78. C33 | C2×SD16 | semidirect |
| 93. Dic6 | C2×C3⋊D3 | semidirect |
| 99. C2×C32 | #214 | semidirect |
| 100. C2×C32 | #215 | semidirect |
| 125. C32 | C2×#214 | semidirect |
| 126. C32 | C2×#215 | semidirect |
| 138. C2×C3 | #3715 | semidirect |
| 139. C2×C3 | #3755 | semidirect |
| 150. C3 | C2×#3715 | semidirect |
| 151. C3 | C2×#3755 | semidirect |
| 153. C2 | #88793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊(C3⋊D3) | 2 |
| C2×C32×Dic6 | 2 |
| C2×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #88793 | 2 |
| C2×#3755 | 3 |
| C2×#3715 | 3 |