Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C3×#261 | C2 | semidirect |
| 3. C3×C22⋊#261 | C2 | semidirect |
| 4. C3×C4⋊#261 | C2 | semidirect |
| 5. C3×C4×#261 | C2 | semidirect |
| 6. D4×#261 | C3 | direct (N × H) |
| 12. C3×D4×C13 | C4 | semidirect |
| 13. C3×C22⋊D13 | C4 | semidirect |
| 14. C3×D52 | C4 | semidirect |
| 16. C22×#261 | C2×C3 | semidirect |
| 18. C22⋊#261 | C2×C3 | semidirect |
| 19. C4⋊#261 | C2×C3 | semidirect |
| 20. C4×#261 | C2×C3 | semidirect |
| 21. C22×C3×C13 | C2×C4 | semidirect |
| 24. C2×C3×D13 | C2×C4 | semidirect |
| 28. C3×#261 | D4 | direct (N × H) |
| 29. C3×C4×C13 | C2×C4 | semidirect |
| 30. C3×Dic13 | C2×C4 | semidirect |
| 36. D4×C13 | C3×C4 | semidirect |
| 37. C22⋊D13 | C3×C4 | semidirect |
| 38. D52 | C3×C4 | semidirect |
| 46. C22×C13 | C2×C3×C4 | semidirect |
| 49. C2×D13 | C2×C3×C4 | semidirect |
| 53. #261 | C3×D4 | direct (N × H) |
| 54. C4×C13 | C2×C3×C4 | semidirect |
| 55. Dic13 | C2×C3×C4 | semidirect |
| 61. C3×C13 | C4×D4 | semidirect |
| 71. C3×D4 | #261 | direct (N × H) |
| 82. C13 | C3×C4×D4 | semidirect |
| 87. C22×C3 | C2×#261 | semidirect |
| 92. C3×C4 | C2×#261 | semidirect |
| 96. D4 | C3×#261 | direct (N × H) |
| 111. C22 | C2×C3×#261 | semidirect |
| 116. C4 | C2×C3×#261 | semidirect |
| 117. C3 | D4×#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#261 | 2 |
| C3×D4×D13 | 2 |
| C3×C22⋊#261 | 2 |
| C3×C4⋊#261 | 2 |
| C3×C4×#261 | 2 |
| D4×#261 | 3 |
| C3×C4×D4 | 13 |