Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D3×D13 |
| commutator, socle, cosocle | C2×C3×C13 | C24 |
| Frattini | C2 | C22×D3×D13 |
| Fitting | C2×C3×C4×C13 | C22 |
| hypercenter | C2×C4 | D3×D13 |
| hypocenter | C3×C13 | C2×#41 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10597790 | C2 | semidirect |
| 2. C2×C4×D3×C13 | C2 | semidirect |
| 3. C3×#6127 | C2 | semidirect |
| 4. D3×C22⋊D13 | C2 | semidirect |
| 5. #10597745 | C2 | semidirect |
| 6. D3×D52 | C2 | semidirect |
| 7. C4×D3×D13 | C2 | semidirect |
| 8. #10597737 | C2 | semidirect |
| 9. #10597735 | C2 | semidirect |
| 10. D3×Dic26 | C2 | semidirect |
| 11. #10597731 | C2 | semidirect |
| 15. C2×C3×C4×C13 | C22 | semidirect |
| 16. #64625 | C22 | semidirect |
| 17. D156 | C22 | semidirect |
| 18. C4×D39 | C22 | semidirect |
| 19. Dic78 | C22 | semidirect |
| 20. C2×Dic3×C13 | C22 | semidirect |
| 23. C4×D3×C13 | C22 | semidirect |
| 24. C4×D3×C13 | C22 | semidirect |
| 25. C3×C22⋊D13 | C22 | semidirect |
| 26. C3×D52 | C22 | semidirect |
| 27. C3×C4×D13 | C22 | semidirect |
| 28. C3×Dic26 | C22 | semidirect |
| 29. #64605 | C22 | semidirect |
| 30. #64604 | C22 | semidirect |
| 31. #64603 | C22 | semidirect |
| 32. #64602 | C22 | semidirect |
| 33. #64601 | C22 | semidirect |
| 35. Dic3×D13 | C22 | semidirect |
| 43. #6127 | D3 | direct (N × H) |
| 67. C2×C4×C13 | C2×D3 | semidirect |
| 71. C22⋊D13 | C2×D3 | semidirect |
| 75. D52 | C2×D3 | semidirect |
| 79. C4×D13 | C2×D3 | semidirect |
| 82. Dic26 | C2×D3 | semidirect |
| 89. D3×C13 | #41 | semidirect |
| 113. C2×C4×D3 | D13 | semidirect |
| 114. C3×C13 | C2×#41 | semidirect |
| 128. C2×C3×C4 | C2×D13 | semidirect |
| 133. C2×Dic3 | C2×D13 | semidirect |
| 141. C4×D3 | C2×D13 | semidirect |
| 142. C4×D3 | C2×D13 | semidirect |
| 156. C13 | D3×#41 | semidirect |
| 192. C2×C4 | D3×D13 | semidirect |
| 198. D3 | #6127 | direct (N × H) |
| 212. C3 | C2×#6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597790 | 2 |
| C2×C4×D3×C13 | 2 |
| C3×#6127 | 2 |
| D3×C22⋊D13 | 2 |
| #10597745 | 2 |
| D3×D52 | 2 |
| C4×D3×D13 | 2 |
| #10597737 | 2 |
| #10597735 | 2 |
| D3×Dic26 | 2 |
| #10597731 | 2 |
| C2×#6127 | 3 |
| D3×#41 | 13 |