Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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. #10597794 | C2 | semidirect |
| 2. D4×D39 | C2 | semidirect |
| 3. C3×C13×SD16 | C2 | semidirect |
| 4. #10597669 | C2 | semidirect |
| 5. #10597667 | C2 | semidirect |
| 6. D312 | C2 | semidirect |
| 7. #10597657 | C2 | semidirect |
| 10. C3×Q8×C13 | C22 | semidirect |
| 15. D156 | C22 | semidirect |
| 18. C3×C8×C13 | C22 | semidirect |
| 19. C3⋊#1055 | C22 | semidirect |
| 22. C13×SD16 | D3 | semidirect |
| 36. Q8×C13 | C2×D3 | semidirect |
| 44. C8×C13 | C2×D3 | semidirect |
| 62. C3×SD16 | D13 | semidirect |
| 67. C3×C13 | AGL(1,ℤ/8) | semidirect |
| 75. C3×Q8 | C2×D13 | semidirect |
| 83. C3×C8 | C2×D13 | semidirect |
| 88. SD16 | D39 | semidirect |
| 92. C13 | #914 | semidirect |
| 102. Q8 | C2×D39 | semidirect |
| 111. C8 | C2×D39 | semidirect |
| 125. C3 | #88168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597794 | 2 |
| D4×D39 | 2 |
| C3×C13×SD16 | 2 |
| #10597669 | 2 |
| #10597667 | 2 |
| D312 | 2 |
| #10597657 | 2 |
| #88168 | 3 |
| #914 | 13 |