Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
402 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 104 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. C3×#3715 | C2 | direct (N × H) |
| 7. C2×#3715 | C3 | direct (N × H) |
| 14. C32×Dic6 | C22 | semidirect |
| 15. C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 22. C2×C3×Dic6 | D3 | semidirect |
| 23. C2×C3×Dic6 | C2×C3 | semidirect |
| 24. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 30. #3715 | C2×C3 | direct (N × H) |
| 69. C3×Dic6 | C2×D3 | semidirect |
| 70. C3×Dic6 | C22×C3 | semidirect |
| 71. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 75. C2×C33 | SD16 | semidirect |
| 85. C2×Dic6 | C3×D3 | semidirect |
| 127. C33 | C2×SD16 | semidirect |
| 158. Dic6 | C2×C3×D3 | semidirect |
| 172. C2×C32 | #214 | semidirect |
| 173. C2×C32 | #215 | semidirect |
| 174. C2×C32 | C3×SD16 | semidirect |
| 222. C32 | C2×#214 | semidirect |
| 223. C32 | C2×#215 | semidirect |
| 224. C32 | C2×C3×SD16 | semidirect |
| 244. C2×C3 | #3715 | direct (N × H) |
| 245. C2×C3 | C3×#214 | semidirect |
| 246. C2×C3 | C3×#215 | semidirect |
| 261. C3 | C2×#3715 | direct (N × H) |
| 262. C3 | C2×C3×#214 | semidirect |
| 263. C3 | C2×C3×#215 | semidirect |
| 265. C2 | C3×#3715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D12 | 2 |
| C2×C32×Dic6 | 2 |
| C2×C3×C3⋊(C3⋊C8) | 2 |
| C3×#3715 | 2 |
| C2×C3×#215 | 3 |
| C2×C3×#214 | 3 |
| C2×#3715 | 3 |