Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
386 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 103 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×C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. #88809 | C2 | direct (N × H) |
| 11. C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 15. C2×C3⋊(C3⋊C8) | D3 | semidirect |
| 46. C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 50. C2×C33 | M16 | semidirect |
| 87. C33 | C2×M16 | semidirect |
| 115. C2×C32 | ΓL(1,𝔽25) | semidirect |
| 116. C2×C32 | #208 | semidirect |
| 152. C32 | C2×ΓL(1,𝔽25) | semidirect |
| 153. C32 | C2×#208 | semidirect |
| 167. C2×C3 | #3711 | semidirect |
| 168. C2×C3 | #3712 | semidirect |
| 182. C3 | C2×#3711 | semidirect |
| 183. C3 | C2×#3712 | semidirect |
| 185. C2 | #88809 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C3⋊D3 | 2 |
| C2×C3×C3⋊(C3⋊C8) | 2 |
| #88809 | 2 |
| C2×#3712 | 3 |
| C2×#3711 | 3 |