Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 124 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. C3×#6127 | C2 | semidirect |
| 3. C3×#6107 | C2 | semidirect |
| 4. C3×#6106 | C2 | semidirect |
| 5. C3×#6105 | C2 | semidirect |
| 6. C3×#6104 | C2 | semidirect |
| 7. C2×C3×#1055 | C2 | semidirect |
| 8. #88204 | C3 | direct (N × H) |
| 20. C13×#41 | C2×C3 | semidirect |
| 21. #6127 | C2×C3 | semidirect |
| 22. #6107 | C2×C3 | semidirect |
| 23. #6106 | C2×C3 | semidirect |
| 24. #6105 | C2×C3 | semidirect |
| 25. #6104 | C2×C3 | semidirect |
| 26. C2×#1055 | C2×C3 | semidirect |
| 58. C3×#41 | D13 | semidirect |
| 64. C3×C13 | #135 | semidirect |
| 82. #41 | C3×D13 | semidirect |
| 88. C13 | C3×#135 | semidirect |
| 118. C3 | #88204 | 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×#6127 | 2 |
| C3×#6107 | 2 |
| C3×#6106 | 2 |
| C3×#6105 | 2 |
| C3×#6104 | 2 |
| C2×C3×#1055 | 2 |
| #88204 | 3 |
| C3×#135 | 13 |