Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
472 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×#261 |
| commutator, hypocenter | C3×C13 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C13 | C2×C4 |
| prime radical | C22×D3×D13 | C2 |
| cosocle | C3×D13 | C24 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C3⋊#261 | C2 | semidirect |
| 3. C22×C3×#261 | C2 | semidirect |
| 4. C2×D3×#261 | C2 | direct (N × H) |
| 6. C22×D39 | C4 | semidirect |
| 7. C22×D3×C13 | C4 | semidirect |
| 9. C2×D3×D13 | C4 | semidirect |
| 11. C2×C3⋊#261 | C22 | semidirect |
| 12. C2×C3×#261 | C22 | semidirect |
| 13. D3×#261 | C22 | direct (N × H) |
| 17. C22×#261 | D3 | direct (N × H) |
| 18. C22×C3×C13 | C2×C4 | semidirect |
| 19. C2×D39 | C2×C4 | semidirect |
| 20. C2×D3×C13 | C2×C4 | semidirect |
| 21. C2×C3×D13 | C2×C4 | semidirect |
| 23. D3×D13 | C2×C4 | semidirect |
| 25. C3⋊#261 | C23 | semidirect |
| 26. C3×#261 | C23 | semidirect |
| 34. C2×#261 | C2×D3 | direct (N × H) |
| 36. C2×C3×C13 | C22×C4 | semidirect |
| 37. D39 | C22×C4 | semidirect |
| 38. C3×D13 | C22×C4 | semidirect |
| 40. D3×C13 | C22×C4 | semidirect |
| 42. C22×C13 | C4×D3 | semidirect |
| 46. C2×D13 | C4×D3 | semidirect |
| 49. #261 | C22×D3 | direct (N × H) |
| 54. C3×C13 | C23×C4 | semidirect |
| 57. C2×C13 | C2×C4×D3 | semidirect |
| 59. D13 | C2×C4×D3 | semidirect |
| 65. C22×D3 | #261 | direct (N × H) |
| 73. C13 | C22×C4×D3 | semidirect |
| 76. C22×C3 | C2×#261 | semidirect |
| 80. C2×D3 | C2×#261 | direct (N × H) |
| 93. C2×C3 | C22×#261 | semidirect |
| 95. D3 | C22×#261 | direct (N × H) |
| 102. C22 | D3×#261 | direct (N × H) |
| 105. C3 | C23×#261 | semidirect |
| 110. C2 | C2×D3×#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×D13 | 2 |
| C22×C3⋊#261 | 2 |
| C22×C3×#261 | 2 |
| C2×D3×#261 | 2 |
| C23×#261 | 3 |
| C22×C4×D3 | 13 |