Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
282 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C2×C32×C4 | C22 |
| commutator | C2 | C22×C32×C4 |
| Frattini, cosocle | C22 | C23×C32 |
| socle | C22×C32 | C23 |
| prime radical | C2×C32×D4 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C32×C4 | C2 | semidirect |
| 3. C32×C4⋊C4 | C2 | semidirect |
| 4. C32×C22⋊C4 | C2 | semidirect |
| 5. C32×C42 | C2 | semidirect |
| 6. C3×C4×D4 | C3 | direct (N × H) |
| 8. C32×D4 | C4 | direct (N × H) |
| 15. C22×C3×C4 | C2×C3 | semidirect |
| 16. C3×C4⋊C4 | C2×C3 | semidirect |
| 17. C3×C22⋊C4 | C2×C3 | semidirect |
| 18. C3×C42 | C2×C3 | semidirect |
| 21. C22×C32 | C2×C4 | semidirect |
| 25. C32×C4 | C2×C4 | semidirect |
| 26. C32×C4 | D4 | direct (N × H) |
| 27. C4×D4 | C32 | direct (N × H) |
| 29. C3×D4 | C3×C4 | direct (N × H) |
| 40. C22×C4 | C2×C32 | semidirect |
| 41. C4⋊C4 | C2×C32 | semidirect |
| 42. C22⋊C4 | C2×C32 | semidirect |
| 43. C42 | C2×C32 | semidirect |
| 46. C22×C3 | C2×C3×C4 | semidirect |
| 50. C3×C4 | C2×C3×C4 | semidirect |
| 51. C3×C4 | C3×D4 | direct (N × H) |
| 52. C32 | C4×D4 | direct (N × H) |
| 54. D4 | C32×C4 | direct (N × H) |
| 66. C22 | C2×C32×C4 | semidirect |
| 70. C4 | C2×C32×C4 | semidirect |
| 71. C4 | C32×D4 | direct (N × H) |
| 72. C3 | C3×C4×D4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D4 | 2 |
| C22×C32×C4 | 2 |
| C32×C4⋊C4 | 2 |
| C32×C22⋊C4 | 2 |
| C32×C42 | 2 |
| C3×C4×D4 | 3 |