Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
260 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 4. #63649 | C3 | direct (N × H) |
| 51. C33 | #108 | semidirect |
| 81. C32 | #822 | semidirect |
| 82. C32 | C3×#108 | semidirect |
| 97. C3 | C3×#822 | semidirect |
| 98. C3 | #63649 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×M16 | 2 |
| C3×#3748 | 2 |
| C2×C3×C3⋊(C3⋊C8) | 2 |
| #63649 | 3 |
| C3×#822 | 3 |