Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #20268157 | C2 | semidirect |
| 3. #20268153 | C2 | semidirect |
| 4. #20268148 | C2 | semidirect |
| 5. #20268139 | C2 | semidirect |
| 6. #20267795 | C2 | semidirect |
| 7. #20267790 | C2 | semidirect |
| 8. #20267785 | C2 | semidirect |
| 9. C2×#15692941 | C2 | semidirect |
| 10. #20267747 | C2 | semidirect |
| 11. #544×C103 | C2 | semidirect |
| 21. #15692944 | C22 | semidirect |
| 22. #15692944 | C22 | semidirect |
| 23. #15692944 | C22 | semidirect |
| 28. #15692941 | C22 | semidirect |
| 29. #15692941 | C22 | semidirect |
| 30. #15692941 | C22 | semidirect |
| 31. #15692932 | C22 | semidirect |
| 32. C4×C103⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C103 | C22 | semidirect |
| 36. #125×C103 | C22 | semidirect |
| 136. C103 | #3136 | semidirect |
| 137. #544 | D103 | semidirect |
| 153. C4⋊Q8 | C2×D103 | semidirect |
| 156. #125 | C2×D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268360 | 2 |
| #20268157 | 2 |
| #20268153 | 2 |
| #20268148 | 2 |
| #20268139 | 2 |
| #20267795 | 2 |
| #20267790 | 2 |
| #20267785 | 2 |
| C2×#15692941 | 2 |
| #20267747 | 2 |
| #544×C103 | 2 |
| #3136 | 103 |