Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20268589 | C2 | semidirect |
| 2. C2×#15693047 | C2 | semidirect |
| 3. #20268558 | C2 | semidirect |
| 4. #20268059 | C2 | semidirect |
| 5. #20268052 | C2 | semidirect |
| 6. #20267839 | C2 | semidirect |
| 7. #20267773 | C2 | semidirect |
| 8. C2×#15692938 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C103 | C2 | semidirect |
| 12. #15693051 | C22 | semidirect |
| 16. #15693046 | C22 | semidirect |
| 18. C2×#13110093 | C22 | semidirect |
| 19. C2×#13110090 | C22 | semidirect |
| 21. #15693028 | C22 | semidirect |
| 26. #15692956 | C22 | semidirect |
| 27. #15692939 | C22 | semidirect |
| 28. #15692938 | C22 | semidirect |
| 29. #15692937 | C22 | semidirect |
| 148. C103 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268589 | 2 |
| C2×#15693047 | 2 |
| #20268558 | 2 |
| #20268059 | 2 |
| #20268052 | 2 |
| #20267839 | 2 |
| #20267773 | 2 |
| C2×#15692938 | 2 |
| C2×AGL(1,ℤ/8)×C103 | 2 |
| #3068 | 103 |