Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20268502 | C2 | semidirect |
| 3. #20268139 | C2 | semidirect |
| 4. #20268111 | C2 | semidirect |
| 5. #20268021 | C2 | semidirect |
| 6. #20267992 | C2 | semidirect |
| 7. #20267943 | C2 | semidirect |
| 8. C4×#13110093 | C2 | semidirect |
| 9. #20267856 | C2 | semidirect |
| 10. #102×D103 | C2 | semidirect |
| 11. #476×C103 | C2 | semidirect |
| 14. C2×#13110094 | C22 | semidirect |
| 16. C2×C8×D103 | C22 | semidirect |
| 19. #15693001 | C22 | semidirect |
| 24. C4×Dic206 | C22 | semidirect |
| 27. C4⋊C4×D103 | C22 | semidirect |
| 28. #15692952 | C22 | semidirect |
| 29. #15692944 | C22 | semidirect |
| 30. #15692943 | C22 | semidirect |
| 32. #15692941 | C22 | semidirect |
| 33. #15692941 | C22 | semidirect |
| 34. (C2×D103)⋊C8 | C22 | semidirect |
| 35. C4×C103⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C103 | C22 | semidirect |
| 38. #106×C103 | C22 | semidirect |
| 39. C4⋊C8×C103 | C22 | semidirect |
| 101. D412 | SD16 | semidirect |
| 137. C103 | #3295 | semidirect |
| 142. #476 | D103 | semidirect |
| 154. C4⋊Q8 | C2×D103 | semidirect |
| 168. #106 | C2×D103 | semidirect |
| 169. C4⋊C8 | C2×D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268502 | 2 |
| D4×D412 | 2 |
| #20268139 | 2 |
| #20268111 | 2 |
| #20268021 | 2 |
| #20267992 | 2 |
| #20267943 | 2 |
| C4×#13110093 | 2 |
| #20267856 | 2 |
| #102×D103 | 2 |
| #476×C103 | 2 |
| #3295 | 103 |