Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
318 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 100 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. C3×C8×C3⋊D3 | C2 | semidirect |
| 3. C32×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C3×#3712 | C2 | semidirect |
| 5. C3×D3×C3⋊C8 | C2 | semidirect |
| 7. #63805 | C3 | direct (N × H) |
| 19. C8×C3⋊D3 | C2×C3 | semidirect |
| 23. C3×ΓL(1,𝔽25) | D3 | semidirect |
| 24. C3×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 28. #3712 | C2×C3 | semidirect |
| 29. D3×C3⋊C8 | C2×C3 | semidirect |
| 76. ΓL(1,𝔽25) | C3×D3 | semidirect |
| 100. C33 | #131 | semidirect |
| 166. C32 | #907 | semidirect |
| 167. C32 | C3×#131 | semidirect |
| 196. C3 | #63805 | direct (N × H) |
| 197. C3 | C3×#907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3798 | 2 |
| C3×C8×C3⋊D3 | 2 |
| C32×ΓL(1,𝔽25) | 2 |
| C3×#3712 | 2 |
| C3×D3×C3⋊C8 | 2 |
| C3×#907 | 3 |
| #63805 | 3 |