Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#15691885 | C2 | semidirect |
| 2. C2×D4×D199 | C2 | semidirect |
| 3. #20263979 | C2 | direct (N × H) |
| 4. C2×#15691875 | C2 | semidirect |
| 5. C2×#15691874 | C2 | semidirect |
| 6. C2×#15691871 | C2 | semidirect |
| 7. C2×#15691869 | C2 | semidirect |
| 8. C2×D8×C199 | C2 | semidirect |
| 11. #15691885 | C22 | semidirect |
| 12. C2×Dic398 | C22 | semidirect |
| 17. D4×D199 | C22 | semidirect |
| 20. #15691875 | C22 | semidirect |
| 21. #15691874 | C22 | semidirect |
| 22. #15691871 | C22 | semidirect |
| 23. #15691869 | C22 | semidirect |
| 24. C2×C199⋊C8 | C22 | semidirect |
| 26. C2×D4×C199 | C22 | semidirect |
| 27. D8×C199 | C22 | semidirect |
| 28. C2×C8×C199 | C22 | semidirect |
| 34. Dic398 | C23 | semidirect |
| 44. C199⋊C8 | C23 | semidirect |
| 50. D4×C199 | C23 | semidirect |
| 52. C8×C199 | C23 | semidirect |
| 69. C2×C199 | AGL(1,ℤ/8) | semidirect |
| 73. C199 | C2×AGL(1,ℤ/8) | semidirect |
| 81. C2×D8 | D199 | semidirect |
| 93. C2×D4 | C2×D199 | semidirect |
| 99. D8 | C2×D199 | semidirect |
| 102. C2×C8 | C2×D199 | semidirect |
| 118. D4 | C22×D199 | semidirect |
| 126. C8 | C22×D199 | semidirect |
| 145. C2 | #20263979 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691885 | 2 |
| C2×D4×D199 | 2 |
| #20263979 | 2 |
| C2×#15691875 | 2 |
| C2×#15691874 | 2 |
| C2×#15691871 | 2 |
| C2×#15691869 | 2 |
| C2×D8×C199 | 2 |
| C2×AGL(1,ℤ/8) | 199 |