Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 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×C22⋊D13 | C2 | semidirect |
| 3. C22×C3×Dic13 | C2 | semidirect |
| 4. C3×#6129 | C2 | direct (N × H) |
| 5. C2×C3×C4×D13 | C2 | semidirect |
| 6. C2×C3×Dic26 | C2 | semidirect |
| 7. C2×#6129 | C3 | direct (N × H) |
| 10. C3×D4×C13 | C22 | semidirect |
| 12. C3×C22⋊D13 | C22 | semidirect |
| 15. C2×C3×Dic13 | C22 | semidirect |
| 16. C3×C4×D13 | C22 | semidirect |
| 17. C3×Dic26 | C22 | semidirect |
| 18. C2×D4×C13 | C2×C3 | semidirect |
| 19. C2×C22⋊D13 | C2×C3 | semidirect |
| 20. C22×Dic13 | C2×C3 | semidirect |
| 21. #6129 | C2×C3 | direct (N × H) |
| 22. C2×C4×D13 | C2×C3 | semidirect |
| 23. C2×Dic26 | C2×C3 | semidirect |
| 34. D4×C13 | C22×C3 | semidirect |
| 36. C22⋊D13 | C22×C3 | semidirect |
| 39. C2×Dic13 | C22×C3 | semidirect |
| 40. C4×D13 | C22×C3 | semidirect |
| 41. Dic26 | C22×C3 | semidirect |
| 44. C2×C3×C13 | #41 | semidirect |
| 58. C2×C3×D4 | D13 | semidirect |
| 61. C3×C13 | C2×#41 | semidirect |
| 64. C2×C13 | C3×#41 | semidirect |
| 71. C3×D4 | C2×D13 | semidirect |
| 80. C2×D4 | C3×D13 | semidirect |
| 83. C13 | C2×C3×#41 | semidirect |
| 96. D4 | C2×C3×D13 | semidirect |
| 104. C2×C3 | #6129 | direct (N × H) |
| 114. C3 | C2×#6129 | direct (N × H) |
| 117. C2 | C3×#6129 | 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×C22⋊D13 | 2 |
| C22×C3×Dic13 | 2 |
| C3×#6129 | 2 |
| C2×C3×C4×D13 | 2 |
| C2×C3×Dic26 | 2 |
| C2×#6129 | 3 |
| C2×C3×#41 | 13 |