Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 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×#15693067 | C2 | semidirect |
| 2. C2×#15693046 | C2 | semidirect |
| 3. C22×D824 | C2 | semidirect |
| 4. #20268360 | C2 | semidirect |
| 5. #20267939 | C2 | semidirect |
| 6. #20267926 | C2 | semidirect |
| 7. #20267795 | C2 | semidirect |
| 8. #20267757 | C2 | semidirect |
| 9. #416×C103 | C2 | semidirect |
| 12. C2×#13110106 | C22 | semidirect |
| 17. C22×D412 | C22 | semidirect |
| 19. C2×D4×D103 | C22 | semidirect |
| 21. C2×#13110092 | C22 | semidirect |
| 23. C2×D824 | C22 | semidirect |
| 24. C2×#13110090 | C22 | semidirect |
| 25. C2×#13110089 | C22 | semidirect |
| 28. #15692996 | C22 | semidirect |
| 30. #15692941 | C22 | semidirect |
| 31. (C2×D103)⋊C8 | C22 | semidirect |
| 33. C22×C8×C103 | C22 | semidirect |
| 34. #117×C103 | C22 | semidirect |
| 35. #103×C103 | C22 | semidirect |
| 36. #102×C103 | C22 | semidirect |
| 55. C2×D412 | D4 | semidirect |
| 72. #41×C103 | D4 | semidirect |
| 152. C103 | #3008 | semidirect |
| 160. #416 | D103 | semidirect |
| 179. C22×C8 | C2×D103 | semidirect |
| 184. #117 | C2×D103 | semidirect |
| 185. #103 | C2×D103 | semidirect |
| 187. #102 | C2×D103 | semidirect |
| 198. #41 | D412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693067 | 2 |
| C2×#15693046 | 2 |
| C22×D824 | 2 |
| #20268360 | 2 |
| #20267939 | 2 |
| #20267926 | 2 |
| #20267795 | 2 |
| #20267757 | 2 |
| #416×C103 | 2 |
| #3008 | 103 |