Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
134 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 74 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. C32×M16 | C2 | semidirect |
| 3. C2×C3×C3⋊C8 | C2 | semidirect |
| 4. C3×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C3×D3×C8 | C2 | semidirect |
| 7. #907 | C3 | direct (N × H) |
| 20. C3×M16 | D3 | semidirect |
| 21. C3×M16 | C2×C3 | semidirect |
| 24. C2×C3⋊C8 | C2×C3 | semidirect |
| 25. ΓL(1,𝔽25) | C2×C3 | semidirect |
| 26. D3×C8 | C2×C3 | semidirect |
| 56. M16 | C3×D3 | semidirect |
| 72. C32 | #131 | semidirect |
| 95. C3 | #907 | direct (N × H) |
| 96. C3 | C3×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#235 | 2 |
| C32×M16 | 2 |
| C2×C3×C3⋊C8 | 2 |
| C3×ΓL(1,𝔽25) | 2 |
| C3×D3×C8 | 2 |
| C3×#131 | 3 |
| #907 | 3 |