Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 80 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. C32×#239 | C2 | semidirect |
| 2. C3×#3799 | C2 | semidirect |
| 3. C3×#3755 | C2 | semidirect |
| 4. C32×#216 | C2 | semidirect |
| 5. C3×#3715 | C2 | semidirect |
| 6. C3×#3714 | C2 | semidirect |
| 7. C3×D3×C3⋊C8 | C2 | semidirect |
| 10. #63949 | C3 | direct (N × H) |
| 25. C3×#239 | D3 | semidirect |
| 26. C3×#239 | C2×C3 | semidirect |
| 28. #3799 | C2×C3 | semidirect |
| 30. #3755 | C2×C3 | semidirect |
| 32. C3×#216 | D3 | semidirect |
| 33. C3×#216 | C2×C3 | semidirect |
| 43. #3715 | C2×C3 | semidirect |
| 44. #3714 | C2×C3 | semidirect |
| 45. D3×C3⋊C8 | C2×C3 | semidirect |
| 110. #239 | C3×D3 | semidirect |
| 119. #216 | C3×D3 | semidirect |
| 164. C33 | #135 | semidirect |
| 274. C32 | #919 | semidirect |
| 275. C32 | #950 | semidirect |
| 276. C32 | C3×#135 | semidirect |
| 318. C3 | #63949 | direct (N × H) |
| 319. C3 | C3×#919 | semidirect |
| 320. C3 | C3×#950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#239 | 2 |
| C3×#3799 | 2 |
| C3×#3755 | 2 |
| C32×#216 | 2 |
| C3×#3715 | 2 |
| C3×#3714 | 2 |
| C3×D3×C3⋊C8 | 2 |
| C3×#950 | 3 |
| C3×#919 | 3 |
| #63949 | 3 |