Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
840 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 263 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×#6308 | C2 | semidirect |
| 3. #88863 | C2 | semidirect |
| 4. #88861 | C2 | semidirect |
| 5. #88855 | C2 | semidirect |
| 52. C33 | #137 | semidirect |
| 76. C32 | #951 | semidirect |
| 95. C3 | #64160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#41 | 2 |
| C2×#6308 | 2 |
| #88863 | 2 |
| #88861 | 2 |
| #88855 | 2 |
| #64160 | 3 |