Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15693048 | C2 | semidirect |
| 2. #20268342 | C2 | semidirect |
| 3. C4×D4×D103 | C2 | semidirect |
| 4. #20268009 | C2 | semidirect |
| 5. #20268008 | C2 | semidirect |
| 6. #20267993 | C2 | semidirect |
| 7. #20267987 | C2 | semidirect |
| 8. #20267986 | C2 | semidirect |
| 9. #20267813 | C2 | semidirect |
| 10. #20267791 | C2 | semidirect |
| 11. #461×C103 | C2 | semidirect |
| 20. #15693018 | C22 | semidirect |
| 21. #15693010 | C22 | semidirect |
| 34. C4⋊(C103⋊C8) | C22 | semidirect |
| 35. Dic103⋊C8 | C22 | semidirect |
| 36. #15692945 | C22 | semidirect |
| 37. #15692943 | C22 | semidirect |
| 38. #15692941 | C22 | semidirect |
| 40. C4⋊Q8×C103 | C22 | semidirect |
| 42. C4⋊C8×C103 | C22 | semidirect |
| 43. #103×C103 | C22 | semidirect |
| 54. D4×D103 | D4 | semidirect |
| 146. C4×C103 | AGL(1,ℤ/8) | semidirect |
| 161. C103 | #3036 | semidirect |
| 168. #461 | D103 | semidirect |
| 182. C4⋊Q8 | C2×D103 | semidirect |
| 200. C4⋊C8 | C2×D103 | semidirect |
| 202. #103 | C2×D103 | semidirect |
| 311. C4 | #15693048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693048 | 2 |
| #20268342 | 2 |
| C4×D4×D103 | 2 |
| #20268009 | 2 |
| #20268008 | 2 |
| #20267993 | 2 |
| #20267987 | 2 |
| #20267986 | 2 |
| #20267813 | 2 |
| #20267791 | 2 |
| #461×C103 | 2 |
| #3036 | 103 |