Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
197 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 54 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×#6180 | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 15. C2×C3⋊(C3⋊C8) | D3 | semidirect |
| 23. C2×(C3⋊D3)⋊C3 | C8 | semidirect |
| 65. C2×C3⋊D3 | C3⋊C8 | semidirect |
| 78. H(3,𝔽3) | C22⋊C8 | semidirect |
| 141. C32 | (C2×D3)⋊C8 | semidirect |
| 142. C32 | #830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×(C3⋊D3)⋊C3 | 2 |
| C2×#6180 | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #63557 | 3 |
| (C2×D3)⋊(C3⋊C8) | 3 |