Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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×C13×#41 | C2 | semidirect |
| 2. C2×C3×D52 | C2 | semidirect |
| 3. C3×#6106 | C2 | semidirect |
| 4. C3×#6104 | C2 | semidirect |
| 5. C3×#6099 | C2 | semidirect |
| 6. #88203 | C3 | direct (N × H) |
| 8. C3×Q8×C13 | C22 | semidirect |
| 10. C3×D4×C13 | C22 | semidirect |
| 15. C3×#1055 | C22 | semidirect |
| 16. C13×#41 | C2×C3 | semidirect |
| 17. C2×D52 | C2×C3 | semidirect |
| 18. #6106 | C2×C3 | semidirect |
| 19. #6104 | C2×C3 | semidirect |
| 20. #6099 | C2×C3 | semidirect |
| 29. Q8×C13 | C22×C3 | semidirect |
| 31. D4×C13 | C22×C3 | semidirect |
| 36. #1055 | C22×C3 | semidirect |
| 49. C3×#41 | D13 | semidirect |
| 54. C3×C13 | AGL(1,ℤ/8) | semidirect |
| 61. C3×Q8 | C2×D13 | semidirect |
| 65. C3×D4 | C2×D13 | semidirect |
| 69. #41 | C3×D13 | semidirect |
| 74. C13 | C3×AGL(1,ℤ/8) | semidirect |
| 83. Q8 | C2×C3×D13 | semidirect |
| 87. D4 | C2×C3×D13 | semidirect |
| 102. C3 | #88203 | 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 |
| C2×C3×D52 | 2 |
| C3×#6106 | 2 |
| C3×#6104 | 2 |
| C3×#6099 | 2 |
| #88203 | 3 |
| C3×AGL(1,ℤ/8) | 13 |