Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
268 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 51. C33 | #108 | semidirect |
| 81. C32 | #822 | semidirect |
| 82. C32 | #822 | semidirect |
| 97. C3 | #63578 | semidirect |
| 98. C3 | #63649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C3×#3748 | 2 |
| C32×#208 | 2 |
| #63649 | 3 |
| #63578 | 3 |