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×#15693045 | C2 | semidirect |
| 2. #20268339 | C2 | semidirect |
| 3. C4×D4×D103 | C2 | semidirect |
| 4. #20268005 | C2 | semidirect |
| 5. #20268004 | C2 | semidirect |
| 6. #20267997 | C2 | semidirect |
| 7. #20267996 | C2 | semidirect |
| 8. #20267983 | C2 | semidirect |
| 9. #20267813 | C2 | semidirect |
| 10. #20267789 | C2 | semidirect |
| 11. #459×C103 | C2 | semidirect |
| 20. #15693021 | C22 | semidirect |
| 21. #15693008 | C22 | semidirect |
| 34. C4⋊(C103⋊C8) | C22 | semidirect |
| 35. Dic103⋊C8 | C22 | semidirect |
| 36. #15692946 | C22 | semidirect |
| 37. #15692944 | C22 | semidirect |
| 38. #15692942 | C22 | semidirect |
| 40. #127×C103 | C22 | semidirect |
| 42. C4⋊C8×C103 | C22 | semidirect |
| 43. #102×C103 | C22 | semidirect |
| 52. D4×D103 | D4 | semidirect |
| 145. C4×C103 | AGL(1,ℤ/8) | semidirect |
| 161. C103 | #3036 | semidirect |
| 170. #459 | D103 | semidirect |
| 183. #127 | C2×D103 | semidirect |
| 200. C4⋊C8 | C2×D103 | semidirect |
| 204. #102 | C2×D103 | semidirect |
| 311. C4 | #15693045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693045 | 2 |
| #20268339 | 2 |
| C4×D4×D103 | 2 |
| #20268005 | 2 |
| #20268004 | 2 |
| #20267997 | 2 |
| #20267996 | 2 |
| #20267983 | 2 |
| #20267813 | 2 |
| #20267789 | 2 |
| #459×C103 | 2 |
| #3036 | 103 |