Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 76 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×#6229 | C2 | semidirect |
| 3. C22⋊C4×H(3,𝔽3) | C2 | semidirect |
| 4. #88552 | C2 | semidirect |
| 5. #88542 | C2 | semidirect |
| 6. #88542 | C2 | semidirect |
| 7. C4×#1084 | C2 | semidirect |
| 20. C32×C22⋊C4 | D3 | semidirect |
| 80. H(3,𝔽3) | #124 | semidirect |
| 109. C22⋊C4 | #272 | semidirect |
| 135. C32 | #885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6235 | 2 |
| C2×#6229 | 2 |
| C22⋊C4×H(3,𝔽3) | 2 |
| #88552 | 2 |
| #88542 | 2 |
| C4×#1084 | 2 |
| C3×#885 | 3 |