Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. C2×C3×C4×D13 | C2 | semidirect |
| 3. C3×C13×C4⋊C4 | C2 | semidirect |
| 4. C3×#6103 | C2 | semidirect |
| 5. C3×C4×Dic13 | C2 | semidirect |
| 6. #88147 | C3 | direct (N × H) |
| 12. C3×D52 | C4 | semidirect |
| 15. C2×C4×D13 | C2×C3 | semidirect |
| 16. C13×C4⋊C4 | C2×C3 | semidirect |
| 17. #6103 | C2×C3 | semidirect |
| 18. C4×Dic13 | C2×C3 | semidirect |
| 22. C2×C3×D13 | C2×C4 | semidirect |
| 24. C3×C4×C13 | C2×C4 | semidirect |
| 26. C3×Dic13 | D4 | semidirect |
| 32. D52 | C3×C4 | semidirect |
| 42. C2×D13 | C2×C3×C4 | semidirect |
| 44. C4×C13 | C2×C3×C4 | semidirect |
| 46. Dic13 | C3×D4 | semidirect |
| 49. C3×C4⋊C4 | D13 | semidirect |
| 52. C3×C13 | C4×D4 | semidirect |
| 67. C4⋊C4 | C3×D13 | semidirect |
| 70. C13 | C3×C4×D4 | semidirect |
| 78. C3×C4 | C4×D13 | semidirect |
| 97. C4 | C3×C4×D13 | semidirect |
| 98. C3 | #88147 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D52 | 2 |
| C2×C3×C4×D13 | 2 |
| C3×C13×C4⋊C4 | 2 |
| C3×#6103 | 2 |
| C3×C4×Dic13 | 2 |
| #88147 | 3 |
| C3×C4×D4 | 13 |