Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
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. #20264001 | C2 | semidirect |
| 2. #20263982 | C2 | semidirect |
| 3. #20263980 | C2 | semidirect |
| 4. #20263978 | C2 | semidirect |
| 5. C2×D1592 | C2 | semidirect |
| 6. D8×D199 | C2 | semidirect |
| 7. #20263961 | C2 | semidirect |
| 8. #135×C199 | C2 | semidirect |
| 9. #15691887 | C22 | semidirect |
| 13. C2×D796 | C22 | semidirect |
| 15. D4×D199 | C22 | semidirect |
| 16. #15691873 | C22 | semidirect |
| 17. D1592 | C22 | semidirect |
| 18. D1592 | C22 | semidirect |
| 19. #15691871 | C22 | semidirect |
| 20. #15691870 | C22 | semidirect |
| 21. #15691869 | C22 | semidirect |
| 22. C8×D199 | C22 | semidirect |
| 23. #41×C199 | C22 | semidirect |
| 24. Q16×C199 | C22 | semidirect |
| 25. SD16×C199 | C22 | semidirect |
| 26. D8×C199 | C22 | semidirect |
| 27. C2×C8×C199 | C22 | semidirect |
| 62. C199 | #576 | semidirect |
| 68. #135 | D199 | semidirect |
| 75. #41 | C2×D199 | semidirect |
| 80. Q16 | C2×D199 | semidirect |
| 82. SD16 | C2×D199 | semidirect |
| 86. D8 | C2×D199 | semidirect |
| 90. C2×C8 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20264001 | 2 |
| #20263982 | 2 |
| #20263980 | 2 |
| #20263978 | 2 |
| C2×D1592 | 2 |
| D8×D199 | 2 |
| #20263961 | 2 |
| #135×C199 | 2 |
| #576 | 199 |