Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C4 | C22×D13 |
| commutator, cosocle | C2×C13 | C24×C3 |
| Frattini | C2 | C23×C3×D13 |
| Fitting | C3×C13×#41 | C2 |
| socle | C2×C3×C13 | C24 |
| hypercenter | C3×#41 | D13 |
| hypocenter | C13 | C2×C3×#41 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C3×C4 ◁ C3×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C13×#41 | C2 | semidirect |
| 2. C3×#6131 | C2 | semidirect |
| 3. C3×Q8×D13 | C2 | semidirect |
| 4. C3×#6129 | C2 | semidirect |
| 5. C3×D4×D13 | C2 | semidirect |
| 6. C3×#6127 | C2 | semidirect |
| 7. C2×C3×C4×D13 | C2 | semidirect |
| 8. #41×D13 | C3 | direct (N × H) |
| 10. C3×Q8×C13 | C22 | semidirect |
| 11. C3×D4×C13 | C22 | semidirect |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 13. C3×C22⋊D13 | C22 | semidirect |
| 14. C2×C3×Dic13 | C22 | semidirect |
| 15. C3×D52 | C22 | semidirect |
| 18. C3×C4×D13 | C22 | semidirect |
| 19. C3×C4×D13 | C22 | semidirect |
| 20. C3×Dic26 | C22 | semidirect |
| 21. C13×#41 | C2×C3 | semidirect |
| 22. #6131 | C2×C3 | semidirect |
| 23. Q8×D13 | C2×C3 | semidirect |
| 24. #6129 | C2×C3 | semidirect |
| 25. D4×D13 | C2×C3 | semidirect |
| 26. #6127 | C2×C3 | semidirect |
| 27. C2×C4×D13 | C2×C3 | semidirect |
| 37. Q8×C13 | C22×C3 | semidirect |
| 38. D4×C13 | C22×C3 | semidirect |
| 39. C2×C4×C13 | C22×C3 | semidirect |
| 40. C22⋊D13 | C22×C3 | semidirect |
| 41. C2×Dic13 | C22×C3 | semidirect |
| 42. D52 | C22×C3 | semidirect |
| 45. C4×D13 | C22×C3 | semidirect |
| 46. C4×D13 | C22×C3 | semidirect |
| 47. Dic26 | C22×C3 | semidirect |
| 52. C3×D13 | #41 | direct (N × H) |
| 64. C3×#41 | D13 | direct (N × H) |
| 68. C3×C13 | C2×#41 | semidirect |
| 73. D13 | C3×#41 | direct (N × H) |
| 76. C3×Q8 | C2×D13 | semidirect |
| 79. C3×D4 | C2×D13 | semidirect |
| 85. C2×C3×C4 | C2×D13 | semidirect |
| 89. #41 | C3×D13 | direct (N × H) |
| 93. C13 | C2×C3×#41 | semidirect |
| 104. Q8 | C2×C3×D13 | semidirect |
| 107. D4 | C2×C3×D13 | semidirect |
| 113. C2×C4 | C2×C3×D13 | semidirect |
| 126. C3 | #41×D13 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C13×#41 | 2 |
| C3×#6131 | 2 |
| C3×Q8×D13 | 2 |
| C3×#6129 | 2 |
| C3×D4×D13 | 2 |
| C3×#6127 | 2 |
| C2×C3×C4×D13 | 2 |
| #41×D13 | 3 |
| C2×C3×#41 | 13 |