Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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. C13×#239 | C2 | semidirect |
| 2. D3×D4×C13 | C2 | semidirect |
| 3. C3×C13×SD16 | C2 | semidirect |
| 4. C13×#215 | C2 | semidirect |
| 5. C13×#213 | C2 | semidirect |
| 6. C13×D24 | C2 | semidirect |
| 7. C13×ΓL(1,𝔽25) | C2 | semidirect |
| 10. C3×Q8×C13 | C22 | semidirect |
| 15. C13×D12 | C22 | semidirect |
| 18. C3×C8×C13 | C22 | semidirect |
| 19. C13×C3⋊C8 | C22 | semidirect |
| 23. C13×SD16 | D3 | semidirect |
| 36. Q8×C13 | C2×D3 | semidirect |
| 45. C8×C13 | C2×D3 | semidirect |
| 46. #914 | C13 | direct (N × H) |
| 60. #239 | C2×C13 | semidirect |
| 61. D3×D4 | C2×C13 | semidirect |
| 62. C3×SD16 | C2×C13 | semidirect |
| 63. #215 | C2×C13 | semidirect |
| 64. #213 | C2×C13 | semidirect |
| 65. D24 | C2×C13 | semidirect |
| 66. ΓL(1,𝔽25) | C2×C13 | semidirect |
| 67. C3×C13 | AGL(1,ℤ/8) | semidirect |
| 75. C3×Q8 | C22×C13 | semidirect |
| 80. D12 | C22×C13 | semidirect |
| 83. C3×C8 | C22×C13 | semidirect |
| 84. C3⋊C8 | C22×C13 | semidirect |
| 88. SD16 | D3×C13 | semidirect |
| 92. C13 | #914 | direct (N × H) |
| 102. Q8 | C2×D3×C13 | semidirect |
| 111. C8 | C2×D3×C13 | semidirect |
| 125. C3 | C13×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#239 | 2 |
| D3×D4×C13 | 2 |
| C3×C13×SD16 | 2 |
| C13×#215 | 2 |
| C13×#213 | 2 |
| C13×D24 | 2 |
| C13×ΓL(1,𝔽25) | 2 |
| C13×AGL(1,ℤ/8) | 3 |
| #914 | 13 |