Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
264 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×C3×C4×C13 | C2 | semidirect |
| 3. C22×C3×Dic13 | C2 | semidirect |
| 4. C3×#6103 | C2 | direct (N × H) |
| 5. C2×#6103 | C3 | direct (N × H) |
| 9. C22×C3×D13 | C4 | semidirect |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 14. C2×C3×Dic13 | C22 | semidirect |
| 16. C22×C4×C13 | C2×C3 | semidirect |
| 17. C22×Dic13 | C2×C3 | semidirect |
| 18. #6103 | C2×C3 | direct (N × H) |
| 26. C2×C3×D13 | C2×C4 | semidirect |
| 32. C22×D13 | C3×C4 | semidirect |
| 35. C2×C4×C13 | C22×C3 | semidirect |
| 37. C2×Dic13 | C22×C3 | semidirect |
| 39. C2×C3×C13 | C22⋊C4 | semidirect |
| 51. C2×D13 | C2×C3×C4 | semidirect |
| 56. C22×C3×C4 | D13 | semidirect |
| 58. C3×C13 | C2×C22⋊C4 | semidirect |
| 60. C2×C13 | C3×C22⋊C4 | semidirect |
| 73. C2×C3×C4 | C2×D13 | semidirect |
| 76. C22×C4 | C3×D13 | semidirect |
| 78. C13 | C2×C3×C22⋊C4 | semidirect |
| 97. C2×C4 | C2×C3×D13 | semidirect |
| 99. C2×C3 | #6103 | direct (N × H) |
| 113. C3 | C2×#6103 | direct (N × H) |
| 115. C2 | C3×#6103 | 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 |
| C22×C3×C4×C13 | 2 |
| C22×C3×Dic13 | 2 |
| C3×#6103 | 2 |
| C2×#6103 | 3 |
| C2×C3×C22⋊C4 | 13 |