Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 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×#15693066 | C2 | semidirect |
| 2. C2×#15693049 | C2 | semidirect |
| 3. C2×#15693017 | C2 | semidirect |
| 4. #20267961 | C2 | direct (N × H) |
| 5. C2×#15692947 | C2 | semidirect |
| 6. C2×#100×C103 | C2 | semidirect |
| 9. #15693066 | C22 | semidirect |
| 12. C22×D412 | C22 | semidirect |
| 17. #15693049 | C22 | semidirect |
| 21. #15693017 | C22 | semidirect |
| 22. C2×C4×Dic103 | C22 | semidirect |
| 23. #15692947 | C22 | semidirect |
| 25. C2×M16×C103 | C22 | semidirect |
| 26. #100×C103 | C22 | semidirect |
| 31. #13110105 | D4 | semidirect |
| 35. C2×Dic206 | D4 | semidirect |
| 39. C2×D412 | D4 | semidirect |
| 40. C2×D412 | C23 | semidirect |
| 55. C4×Dic103 | C23 | semidirect |
| 63. M16×C103 | C23 | semidirect |
| 94. D412 | C2×D4 | semidirect |
| 98. Dic206 | C2×D4 | semidirect |
| 122. C2×C103 | #453 | semidirect |
| 127. C103 | C2×#453 | semidirect |
| 133. C2×#100 | D103 | semidirect |
| 148. C2×M16 | C2×D103 | semidirect |
| 153. #100 | C2×D103 | semidirect |
| 188. M16 | C22×D103 | semidirect |
| 251. C2 | #20267961 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693066 | 2 |
| C2×#15693049 | 2 |
| C2×#15693017 | 2 |
| #20267961 | 2 |
| C2×#15692947 | 2 |
| C2×#100×C103 | 2 |
| C2×#453 | 103 |