Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
366 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×#3828 | C2 | semidirect |
| 2. C32×#235 | C2 | semidirect |
| 3. C2×C32×C3⋊C8 | C2 | semidirect |
| 4. C3×#3719 | C2 | semidirect |
| 5. C3×#3717 | C2 | semidirect |
| 6. C3×#3716 | C2 | semidirect |
| 7. C3×#3714 | C2 | semidirect |
| 10. #63829 | C3 | direct (N × H) |
| 23. #3828 | C2×C3 | semidirect |
| 28. C3×#235 | D3 | semidirect |
| 29. C3×#235 | C2×C3 | semidirect |
| 36. C2×C3×C3⋊C8 | D3 | semidirect |
| 37. C2×C3×C3⋊C8 | C2×C3 | semidirect |
| 42. #3719 | C2×C3 | semidirect |
| 43. #3717 | C2×C3 | semidirect |
| 44. #3716 | C2×C3 | semidirect |
| 45. #3714 | C2×C3 | semidirect |
| 114. #235 | C3×D3 | semidirect |
| 126. C2×C3⋊C8 | C3×D3 | semidirect |
| 169. C33 | #135 | semidirect |
| 287. C32 | #904 | semidirect |
| 288. C32 | #950 | semidirect |
| 289. C32 | C3×#135 | semidirect |
| 334. C3 | #63829 | direct (N × H) |
| 335. C3 | C3×#904 | semidirect |
| 336. C3 | C3×#950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3828 | 2 |
| C32×#235 | 2 |
| C2×C32×C3⋊C8 | 2 |
| C3×#3719 | 2 |
| C3×#3717 | 2 |
| C3×#3716 | 2 |
| C3×#3714 | 2 |
| C3×#950 | 3 |
| C3×#904 | 3 |
| #63829 | 3 |