Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #20268627 | C2 | semidirect |
| 2. #20268606 | C2 | semidirect |
| 3. #20268599 | C2 | semidirect |
| 4. #20268589 | C2 | semidirect |
| 5. C2×#15693052 | C2 | semidirect |
| 6. #20268558 | C2 | semidirect |
| 7. C2×2−1+4×C103 | C2 | semidirect |
| 9. #15693068 | C22 | semidirect |
| 10. #15693067 | C22 | semidirect |
| 14. #15693052 | C22 | semidirect |
| 15. #15693052 | C22 | semidirect |
| 16. #15693051 | C22 | semidirect |
| 17. #15693047 | C22 | semidirect |
| 18. #15693046 | C22 | semidirect |
| 19. #15693041 | C22 | semidirect |
| 20. C2×#13110095 | C22 | semidirect |
| 21. C2×#13110092 | C22 | semidirect |
| 22. #15693028 | C22 | semidirect |
| 23. C2×#13110089 | C22 | semidirect |
| 25. 2−1+4×C103 | C22 | semidirect |
| 28. C2×#41×C103 | C22 | semidirect |
| 30. C22×Q8×C103 | C22 | semidirect |
| 113. C103 | #3586 | semidirect |
| 115. C2×2−1+4 | D103 | semidirect |
| 124. 2−1+4 | C2×D103 | semidirect |
| 131. C2×#41 | C2×D103 | semidirect |
| 133. C22×Q8 | C2×D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268627 | 2 |
| #20268606 | 2 |
| #20268599 | 2 |
| #20268589 | 2 |
| C2×#15693052 | 2 |
| #20268558 | 2 |
| C2×2−1+4×C103 | 2 |
| #3586 | 103 |