Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20268498 | C2 | semidirect |
| 3. #20268138 | C2 | semidirect |
| 4. #20268110 | C2 | semidirect |
| 5. #20268082 | C2 | semidirect |
| 6. #20268020 | C2 | semidirect |
| 7. #20267992 | C2 | semidirect |
| 8. #20267944 | C2 | semidirect |
| 9. C4×#13110094 | C2 | semidirect |
| 10. C2×#15692943 | C2 | semidirect |
| 11. C8×D4×C103 | C2 | semidirect |
| 15. C2×#13110094 | C22 | semidirect |
| 16. #15693021 | C22 | semidirect |
| 19. #15693000 | C22 | semidirect |
| 24. C4×Dic206 | C22 | semidirect |
| 27. C2×C4⋊Dic103 | C22 | semidirect |
| 28. #15692953 | C22 | semidirect |
| 29. #15692953 | C22 | semidirect |
| 30. #15692946 | C22 | semidirect |
| 33. #15692943 | C22 | semidirect |
| 34. #15692943 | C22 | semidirect |
| 35. #15692943 | C22 | semidirect |
| 36. C22×C8×C103 | C22 | semidirect |
| 38. C4⋊C8×C103 | C22 | semidirect |
| 39. C22⋊C8×C103 | C22 | semidirect |
| 40. C4×C8×C103 | C22 | semidirect |
| 83. D4×C103 | SD16 | semidirect |
| 137. C103 | #3295 | semidirect |
| 147. C8×D4 | D103 | semidirect |
| 153. C22×C8 | C2×D103 | semidirect |
| 169. C4⋊C8 | C2×D103 | semidirect |
| 176. C22⋊C8 | C2×D103 | semidirect |
| 177. C4×C8 | C2×D103 | semidirect |
| 231. D4 | #13110094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268498 | 2 |
| D4×D412 | 2 |
| #20268138 | 2 |
| #20268110 | 2 |
| #20268082 | 2 |
| #20268020 | 2 |
| #20267992 | 2 |
| #20267944 | 2 |
| C4×#13110094 | 2 |
| C2×#15692943 | 2 |
| C8×D4×C103 | 2 |
| #3295 | 103 |