Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
146 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×#208 | C2 | semidirect |
| 4. C3×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C3×D3×C8 | C2 | semidirect |
| 7. D3×M16 | C3 | direct (N × H) |
| 15. C32×C8 | C22 | semidirect |
| 16. C3×C3⋊C8 | C22 | semidirect |
| 22. C3×M16 | D3 | direct (N × H) |
| 23. C3×M16 | C2×C3 | semidirect |
| 25. #208 | C2×C3 | semidirect |
| 26. ΓL(1,𝔽25) | C2×C3 | semidirect |
| 27. D3×C8 | C2×C3 | semidirect |
| 54. C3×C8 | C2×D3 | semidirect |
| 55. C3×C8 | C22×C3 | semidirect |
| 56. C3⋊C8 | C22×C3 | semidirect |
| 60. C3×D3 | M16 | direct (N × H) |
| 64. M16 | C3×D3 | direct (N × H) |
| 85. C32 | C2×M16 | semidirect |
| 94. C8 | C2×C3×D3 | semidirect |
| 104. D3 | C3×M16 | direct (N × H) |
| 114. C3 | D3×M16 | direct (N × H) |
| 115. C3 | C2×C3×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D3 | 2 |
| C32×M16 | 2 |
| C3×#208 | 2 |
| C3×ΓL(1,𝔽25) | 2 |
| C3×D3×C8 | 2 |
| C2×C3×M16 | 3 |
| D3×M16 | 3 |