Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20270023 | C2 | semidirect |
| 2. #20270004 | C2 | semidirect |
| 3. #20270002 | C2 | semidirect |
| 4. #20270000 | C2 | semidirect |
| 5. C2×D1688 | C2 | semidirect |
| 6. D8×D211 | C2 | semidirect |
| 7. #20269983 | C2 | semidirect |
| 8. #135×C211 | C2 | semidirect |
| 9. #16809963 | C22 | semidirect |
| 13. C2×D844 | C22 | semidirect |
| 15. D4×D211 | C22 | semidirect |
| 16. #16809949 | C22 | semidirect |
| 17. D1688 | C22 | semidirect |
| 18. D1688 | C22 | semidirect |
| 19. #16809947 | C22 | semidirect |
| 20. #16809946 | C22 | semidirect |
| 21. #16809945 | C22 | semidirect |
| 22. C8×D211 | C22 | semidirect |
| 23. #41×C211 | C22 | semidirect |
| 24. Q16×C211 | C22 | semidirect |
| 25. SD16×C211 | C22 | semidirect |
| 26. D8×C211 | C22 | semidirect |
| 27. C2×C8×C211 | C22 | semidirect |
| 62. C211 | #576 | semidirect |
| 68. #135 | D211 | semidirect |
| 75. #41 | C2×D211 | semidirect |
| 80. Q16 | C2×D211 | semidirect |
| 82. SD16 | C2×D211 | semidirect |
| 86. D8 | C2×D211 | semidirect |
| 90. C2×C8 | C2×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20270023 | 2 |
| #20270004 | 2 |
| #20270002 | 2 |
| #20270000 | 2 |
| C2×D1688 | 2 |
| D8×D211 | 2 |
| #20269983 | 2 |
| #135×C211 | 2 |
| #576 | 211 |