Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 90 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×C4×C13 | C2 | semidirect |
| 3. C2×C4×D3×C13 | C2 | semidirect |
| 4. C13×#217 | C2 | semidirect |
| 5. C13×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C13×Dic3⋊C4 | C2 | semidirect |
| 7. C4×Dic3×C13 | C2 | semidirect |
| 14. C13×#67 | C4 | direct (N × H) |
| 21. C22×C4×C13 | D3 | semidirect |
| 28. C22×C3×C13 | C2×C4 | semidirect |
| 32. C2×D3×C13 | C2×C4 | semidirect |
| 34. C3×C4×C13 | D4 | semidirect |
| 37. Dic3×C13 | C2×C4 | semidirect |
| 48. C4×#67 | C13 | direct (N × H) |
| 59. C22×C13 | C4×D3 | semidirect |
| 65. C4×C13 | #67 | direct (N × H) |
| 66. C22×C3×C4 | C2×C13 | semidirect |
| 68. C2×C4×D3 | C2×C13 | semidirect |
| 69. #217 | C2×C13 | semidirect |
| 70. (C2×D3)⋊C4 | C2×C13 | semidirect |
| 71. Dic3⋊C4 | C2×C13 | semidirect |
| 72. C4×Dic3 | C2×C13 | semidirect |
| 73. C3×C13 | C4×D4 | semidirect |
| 85. #67 | C4×C13 | direct (N × H) |
| 92. C22×C4 | D3×C13 | semidirect |
| 97. C13 | C4×#67 | direct (N × H) |
| 100. C22×C3 | C2×C4×C13 | semidirect |
| 104. C2×D3 | C2×C4×C13 | semidirect |
| 106. C3×C4 | D4×C13 | semidirect |
| 109. Dic3 | C2×C4×C13 | semidirect |
| 130. C22 | C4×D3×C13 | semidirect |
| 136. C4 | C13×#67 | direct (N × H) |
| 137. C3 | C4×D4×C13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C13 | 2 |
| C2×C13×#67 | 2 |
| C2×C4×D3×C13 | 2 |
| C13×#217 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C13×Dic3⋊C4 | 2 |
| C4×Dic3×C13 | 2 |
| C4×D4×C13 | 3 |
| C4×#67 | 13 |