Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15693041 | C2 | semidirect |
| 2. #20268462 | C2 | semidirect |
| 3. #20268167 | C2 | semidirect |
| 4. #20268025 | C2 | semidirect |
| 5. #20267991 | C2 | semidirect |
| 6. #20267988 | C2 | semidirect |
| 7. #20267936 | C2 | semidirect |
| 8. #20267934 | C2 | semidirect |
| 9. C4×#13110095 | C2 | semidirect |
| 10. D4×C103⋊C8 | C2 | semidirect |
| 11. #550×C103 | C2 | semidirect |
| 51. #13110095 | D4 | semidirect |
| 131. C4×C103 | #135 | semidirect |
| 143. C103 | #3287 | semidirect |
| 146. #550 | D103 | semidirect |
| 276. C4 | #15693041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693041 | 2 |
| #20268462 | 2 |
| #20268167 | 2 |
| #20268025 | 2 |
| #20267991 | 2 |
| #20267988 | 2 |
| #20267936 | 2 |
| #20267934 | 2 |
| C4×#13110095 | 2 |
| D4×C103⋊C8 | 2 |
| #550×C103 | 2 |
| #3287 | 103 |