Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
101 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 101 conjugacy classes of subgroups — too many to draw. Only its 26 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. #3746⋊C3 | C2 | semidirect |
| 3. #88386 | C2 | semidirect |
| 9. #3746 | D3 | semidirect |
| 49. H(3,𝔽3) | SD32 | semidirect |
| 79. C32 | #827 | semidirect |
| 80. C32 | #828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3745⋊C3 | 2 |
| #3746⋊C3 | 2 |
| #88386 | 2 |
| #63549 | 3 |
| #63548 | 3 |