Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C3×D4×C13 | C2 | semidirect |
| 2. C2×C3×D52 | C2 | semidirect |
| 3. C3×#6104 | C2 | direct (N × H) |
| 4. C2×C3×#1055 | C2 | semidirect |
| 5. C2×#6104 | C3 | direct (N × H) |
| 9. C3×D4×C13 | C22 | semidirect |
| 12. C3×D52 | C22 | semidirect |
| 13. C3×#1055 | C22 | semidirect |
| 14. C2×D4×C13 | C2×C3 | semidirect |
| 15. C2×D52 | C2×C3 | semidirect |
| 16. #6104 | C2×C3 | direct (N × H) |
| 17. C2×#1055 | C2×C3 | semidirect |
| 28. D4×C13 | C22×C3 | semidirect |
| 31. D52 | C22×C3 | semidirect |
| 32. #1055 | C22×C3 | semidirect |
| 35. C2×C3×C13 | D8 | semidirect |
| 46. C2×C3×D4 | D13 | semidirect |
| 49. C3×C13 | C2×D8 | semidirect |
| 52. C2×C13 | C3×D8 | semidirect |
| 60. C3×D4 | C2×D13 | semidirect |
| 64. C2×D4 | C3×D13 | semidirect |
| 67. C13 | C2×C3×D8 | semidirect |
| 80. D4 | C2×C3×D13 | semidirect |
| 85. C2×C3 | #6104 | direct (N × H) |
| 94. C3 | C2×#6104 | direct (N × H) |
| 97. C2 | C3×#6104 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C13 | 2 |
| C2×C3×D52 | 2 |
| C3×#6104 | 2 |
| C2×C3×#1055 | 2 |
| C2×#6104 | 3 |
| C2×C3×D8 | 13 |