Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15693068 | C2 | semidirect |
| 2. #20268589 | C2 | semidirect |
| 3. #20268362 | C2 | semidirect |
| 4. #20267972 | C2 | semidirect |
| 5. #20267962 | C2 | semidirect |
| 6. #20267808 | C2 | semidirect |
| 7. #20267807 | C2 | semidirect |
| 8. C2×#15692939 | C2 | semidirect |
| 9. #575×C103 | C2 | semidirect |
| 21. #15693052 | C22 | semidirect |
| 23. #15693047 | C22 | semidirect |
| 27. #15693019 | C22 | semidirect |
| 28. #15693008 | C22 | semidirect |
| 32. #15692948 | C22 | semidirect |
| 33. #15692947 | C22 | semidirect |
| 34. #15692939 | C22 | semidirect |
| 38. #137×C103 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C103 | C22 | semidirect |
| 186. C103 | #3020 | semidirect |
| 189. #575 | D103 | semidirect |
| 212. #137 | C2×D103 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693068 | 2 |
| #20268589 | 2 |
| #20268362 | 2 |
| #20267972 | 2 |
| #20267962 | 2 |
| #20267808 | 2 |
| #20267807 | 2 |
| C2×#15692939 | 2 |
| #575×C103 | 2 |
| #3020 | 103 |