Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#15693047 | C2 | semidirect |
| 2. #20268341 | C2 | semidirect |
| 3. #20268178 | C2 | semidirect |
| 4. #20268167 | C2 | semidirect |
| 5. #20268163 | C2 | semidirect |
| 6. C4×#13110089 | C2 | semidirect |
| 7. C2×#127×C103 | C2 | semidirect |
| 10. C2×#13110093 | C22 | semidirect |
| 11. C2×#13110090 | C22 | semidirect |
| 13. #15693021 | C22 | semidirect |
| 14. #15693018 | C22 | semidirect |
| 15. #15693009 | C22 | semidirect |
| 18. #15692932 | C22 | semidirect |
| 19. C4×C103⋊C8 | C22 | semidirect |
| 34. #13110089 | D4 | semidirect |
| 71. C103⋊C8 | C2×D4 | semidirect |
| 82. C4×C103 | AGL(1,ℤ/8) | semidirect |
| 91. C103 | #3151 | semidirect |
| 94. C2×#127 | D103 | semidirect |
| 174. C4 | #15693047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693047 | 2 |
| #20268341 | 2 |
| #20268178 | 2 |
| #20268167 | 2 |
| #20268163 | 2 |
| C4×#13110089 | 2 |
| C2×#127×C103 | 2 |
| #3151 | 103 |