Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 1. C3×#6131 | C2 | semidirect |
| 2. C3×D4×D13 | C2 | semidirect |
| 3. C3×C13×SD16 | C2 | semidirect |
| 4. C3×#6106 | C2 | semidirect |
| 5. C3×#6104 | C2 | semidirect |
| 6. C3×D104 | C2 | semidirect |
| 7. C3×#6094 | C2 | semidirect |
| 8. #88168 | C3 | direct (N × H) |
| 10. C3×Q8×C13 | C22 | semidirect |
| 15. C3×D52 | C22 | semidirect |
| 18. C3×C8×C13 | C22 | semidirect |
| 19. C3×#1055 | C22 | semidirect |
| 20. #6131 | C2×C3 | semidirect |
| 21. D4×D13 | C2×C3 | semidirect |
| 22. C13×SD16 | C2×C3 | semidirect |
| 23. #6106 | C2×C3 | semidirect |
| 24. #6104 | C2×C3 | semidirect |
| 25. D104 | C2×C3 | semidirect |
| 26. #6094 | C2×C3 | semidirect |
| 36. Q8×C13 | C22×C3 | semidirect |
| 41. D52 | C22×C3 | semidirect |
| 44. C8×C13 | C22×C3 | semidirect |
| 45. #1055 | C22×C3 | semidirect |
| 63. C3×SD16 | D13 | semidirect |
| 67. C3×C13 | AGL(1,ℤ/8) | semidirect |
| 75. C3×Q8 | C2×D13 | semidirect |
| 84. C3×C8 | C2×D13 | semidirect |
| 88. SD16 | C3×D13 | semidirect |
| 92. C13 | C3×AGL(1,ℤ/8) | semidirect |
| 102. Q8 | C2×C3×D13 | semidirect |
| 111. C8 | C2×C3×D13 | semidirect |
| 125. C3 | #88168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6131 | 2 |
| C3×D4×D13 | 2 |
| C3×C13×SD16 | 2 |
| C3×#6106 | 2 |
| C3×#6104 | 2 |
| C3×D104 | 2 |
| C3×#6094 | 2 |
| #88168 | 3 |
| C3×AGL(1,ℤ/8) | 13 |