Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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. C23×C3×D13 | C2 | semidirect |
| 2. C2×C3×C22⋊D13 | C2 | semidirect |
| 3. C2×C3×D52 | C2 | semidirect |
| 4. C3×C13×C22⋊C4 | C2 | semidirect |
| 5. C3×#6103 | C2 | semidirect |
| 6. #88136 | C3 | direct (N × H) |
| 11. C22×C3×D13 | C22 | semidirect |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 14. C2×C3×Dic13 | C22 | semidirect |
| 16. C23×D13 | C2×C3 | semidirect |
| 17. C2×C22⋊D13 | C2×C3 | semidirect |
| 18. C2×D52 | C2×C3 | semidirect |
| 19. C13×C22⋊C4 | C2×C3 | semidirect |
| 20. #6103 | C2×C3 | semidirect |
| 22. C22×C3×C13 | D4 | semidirect |
| 29. C2×C3×D13 | D4 | semidirect |
| 36. C22×D13 | C22×C3 | semidirect |
| 37. C2×C4×C13 | C22×C3 | semidirect |
| 39. C2×Dic13 | C22×C3 | semidirect |
| 48. C22×C13 | C3×D4 | semidirect |
| 55. C2×D13 | C3×D4 | semidirect |
| 62. C3×C22⋊C4 | D13 | semidirect |
| 63. C3×C13 | #120 | semidirect |
| 78. C2×C3×C4 | C2×D13 | semidirect |
| 83. C22⋊C4 | C3×D13 | semidirect |
| 84. C13 | C3×#120 | semidirect |
| 92. C22×C3 | D52 | semidirect |
| 104. C2×C4 | C2×C3×D13 | semidirect |
| 117. C22 | C3×D52 | semidirect |
| 121. C3 | #88136 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D13 | 2 |
| C2×C3×C22⋊D13 | 2 |
| C2×C3×D52 | 2 |
| C3×C13×C22⋊C4 | 2 |
| C3×#6103 | 2 |
| #88136 | 3 |
| C3×#120 | 13 |