Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20268608 | C2 | semidirect |
| 2. #20268601 | C2 | semidirect |
| 3. #20268592 | C2 | semidirect |
| 4. #20268174 | C2 | semidirect |
| 5. #20268067 | C2 | semidirect |
| 6. #20268053 | C2 | semidirect |
| 7. #20267971 | C2 | semidirect |
| 8. #20267962 | C2 | semidirect |
| 9. #20267907 | C2 | semidirect |
| 10. #20267906 | C2 | semidirect |
| 11. #472×C103 | C2 | semidirect |
| 12. #15693068 | C22 | semidirect |
| 16. #15693054 | C22 | semidirect |
| 27. C2×Dic412 | C22 | semidirect |
| 28. C2×#13110093 | C22 | semidirect |
| 31. #15693029 | C22 | semidirect |
| 33. #15693008 | C22 | semidirect |
| 34. #15692956 | C22 | semidirect |
| 35. #15692948 | C22 | semidirect |
| 37. #15692947 | C22 | semidirect |
| 38. #15692939 | C22 | semidirect |
| 39. C8×Dic103 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C103 | C22 | semidirect |
| 42. #131×C103 | C22 | semidirect |
| 43. #108×C103 | C22 | semidirect |
| 44. #100×C103 | C22 | semidirect |
| 150. C103 | #3290 | semidirect |
| 156. #472 | D103 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D103 | semidirect |
| 185. #131 | C2×D103 | semidirect |
| 188. #108 | C2×D103 | semidirect |
| 193. #100 | C2×D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268608 | 2 |
| #20268601 | 2 |
| #20268592 | 2 |
| #20268174 | 2 |
| #20268067 | 2 |
| #20268053 | 2 |
| #20267971 | 2 |
| #20267962 | 2 |
| #20267907 | 2 |
| #20267906 | 2 |
| #472×C103 | 2 |
| #3290 | 103 |