Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20270024 | C2 | semidirect |
| 2. #20270023 | C2 | semidirect |
| 3. #20270010 | C2 | semidirect |
| 4. #20270005 | C2 | semidirect |
| 5. #20269999 | C2 | semidirect |
| 6. C2×#16809951 | C2 | semidirect |
| 7. #131×C211 | C2 | semidirect |
| 10. #16809962 | C22 | semidirect |
| 12. C2×Dic422 | C22 | semidirect |
| 16. Dic844 | C22 | semidirect |
| 17. #16809951 | C22 | semidirect |
| 18. #16809951 | C22 | semidirect |
| 19. #16809951 | C22 | semidirect |
| 20. D1688 | C22 | semidirect |
| 22. M16×C211 | C22 | semidirect |
| 23. C2×C8×C211 | C22 | semidirect |
| 53. C211 | #577 | semidirect |
| 61. #131 | D211 | semidirect |
| 76. M16 | C2×D211 | semidirect |
| 77. C2×C8 | C2×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20270024 | 2 |
| #20270023 | 2 |
| #20270010 | 2 |
| #20270005 | 2 |
| #20269999 | 2 |
| C2×#16809951 | 2 |
| #131×C211 | 2 |
| #577 | 211 |