Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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. C23×D3×C13 | C2 | semidirect |
| 2. C2×C3×D4×C13 | C2 | semidirect |
| 3. C2×C13×#67 | C2 | semidirect |
| 4. C13×#217 | C2 | semidirect |
| 5. C13×(C2×D3)⋊C4 | C2 | semidirect |
| 8. C23×C3×C13 | C22 | semidirect |
| 13. C2×C3×C4×C13 | C22 | semidirect |
| 15. C2×Dic3×C13 | C22 | semidirect |
| 18. C2×D4×C13 | D3 | semidirect |
| 24. C22×C3×C13 | D4 | semidirect |
| 29. C2×D3×C13 | D4 | semidirect |
| 36. C23×C13 | C2×D3 | semidirect |
| 40. C2×C4×C13 | C2×D3 | semidirect |
| 41. #937 | C13 | direct (N × H) |
| 54. C22×C13 | #67 | semidirect |
| 58. C23×D3 | C2×C13 | semidirect |
| 59. C2×C3×D4 | C2×C13 | semidirect |
| 60. C2×#67 | C2×C13 | semidirect |
| 61. #217 | C2×C13 | semidirect |
| 62. (C2×D3)⋊C4 | C2×C13 | semidirect |
| 63. C3×C13 | #120 | semidirect |
| 71. C23×C3 | C22×C13 | semidirect |
| 76. C2×C3×C4 | C22×C13 | semidirect |
| 78. C2×Dic3 | C22×C13 | semidirect |
| 81. C2×D4 | D3×C13 | semidirect |
| 84. C13 | #937 | direct (N × H) |
| 88. C22×C3 | D4×C13 | semidirect |
| 93. C2×D3 | D4×C13 | semidirect |
| 100. C23 | C2×D3×C13 | semidirect |
| 104. C2×C4 | C2×D3×C13 | semidirect |
| 117. C22 | C13×#67 | semidirect |
| 121. C3 | C13×#120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D3×C13 | 2 |
| C2×C3×D4×C13 | 2 |
| C2×C13×#67 | 2 |
| C13×#217 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C13×#120 | 3 |
| #937 | 13 |