Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 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 |
|---|---|---|
| 2. C2×#15693054 | C2 | semidirect |
| 3. C2×#15693008 | C2 | semidirect |
| 4. #20267971 | C2 | direct (N × H) |
| 5. C2×#15692947 | C2 | semidirect |
| 6. C2×#100×C103 | C2 | semidirect |
| 12. C22×Dic206 | C22 | semidirect |
| 16. #15693054 | C22 | semidirect |
| 20. #15693008 | C22 | semidirect |
| 22. C2×C4×Dic103 | C22 | semidirect |
| 23. #15692947 | C22 | semidirect |
| 25. C2×M16×C103 | C22 | semidirect |
| 26. #100×C103 | C22 | semidirect |
| 38. C2×Dic206 | C23 | semidirect |
| 54. C4×Dic103 | C23 | semidirect |
| 62. M16×C103 | C23 | semidirect |
| 116. C2×C103 | #455 | semidirect |
| 120. C103 | C2×#455 | semidirect |
| 126. C2×#100 | D103 | semidirect |
| 140. C2×M16 | C2×D103 | semidirect |
| 146. #100 | C2×D103 | semidirect |
| 179. M16 | C22×D103 | semidirect |
| 237. C2 | #20267971 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693066 | 2 |
| C2×#15693054 | 2 |
| C2×#15693008 | 2 |
| #20267971 | 2 |
| C2×#15692947 | 2 |
| C2×#100×C103 | 2 |
| C2×#455 | 103 |