Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 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. C2×#16809962 | C2 | semidirect |
| 2. #20270008 | C2 | semidirect |
| 3. #20270007 | C2 | semidirect |
| 4. #20270003 | C2 | semidirect |
| 5. #20270002 | C2 | semidirect |
| 6. #20269997 | C2 | semidirect |
| 7. C2×#16809946 | C2 | semidirect |
| 8. C2×#41×C211 | C2 | semidirect |
| 12. #16809962 | C22 | semidirect |
| 13. C2×Dic422 | C22 | semidirect |
| 14. C2×D844 | C22 | semidirect |
| 17. #16809952 | C22 | semidirect |
| 18. #16809950 | C22 | semidirect |
| 19. #16809949 | C22 | semidirect |
| 20. #16809947 | C22 | semidirect |
| 21. #16809946 | C22 | semidirect |
| 22. #16809946 | C22 | semidirect |
| 23. C2×C211⋊C8 | C22 | semidirect |
| 27. #41×C211 | C22 | semidirect |
| 28. C2×Q8×C211 | C22 | semidirect |
| 30. C2×D4×C211 | C22 | semidirect |
| 81. C211 | #575 | semidirect |
| 84. C2×#41 | D211 | semidirect |
| 98. #41 | C2×D211 | semidirect |
| 100. C2×Q8 | C2×D211 | semidirect |
| 104. C2×D4 | C2×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16809962 | 2 |
| #20270008 | 2 |
| #20270007 | 2 |
| #20270003 | 2 |
| #20270002 | 2 |
| #20269997 | 2 |
| C2×#16809946 | 2 |
| C2×#41×C211 | 2 |
| #575 | 211 |