Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15693043 | C2 | semidirect |
| 2. #20268302 | C2 | semidirect |
| 3. #20268049 | C2 | semidirect |
| 4. #20268044 | C2 | semidirect |
| 5. #20268037 | C2 | semidirect |
| 6. #20267829 | C2 | semidirect |
| 7. #20267788 | C2 | semidirect |
| 8. C22×M16×C103 | C2 | semidirect |
| 11. C2×Dic412 | C22 | semidirect |
| 12. C2×#13110094 | C22 | semidirect |
| 13. C2×D824 | C22 | semidirect |
| 20. #15692955 | C22 | semidirect |
| 21. #15692953 | C22 | semidirect |
| 22. #15692946 | C22 | semidirect |
| 23. #15692943 | C22 | semidirect |
| 56. C2×C8×C103 | D4 | semidirect |
| 106. C103 | #3054 | semidirect |
| 108. C22×M16 | D103 | semidirect |
| 156. C2×C8 | C22⋊D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693043 | 2 |
| #20268302 | 2 |
| #20268049 | 2 |
| #20268044 | 2 |
| #20268037 | 2 |
| #20267829 | 2 |
| #20267788 | 2 |
| C22×M16×C103 | 2 |
| #3054 | 103 |