Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×Q8×D199 | C2 | semidirect |
| 3. #20263988 | C2 | semidirect |
| 4. #20263987 | C2 | semidirect |
| 5. #20263986 | C2 | semidirect |
| 6. #20263985 | C2 | semidirect |
| 7. #20263984 | C2 | semidirect |
| 8. Q16×D199 | C2 | semidirect |
| 9. SD16×D199 | C2 | semidirect |
| 10. M16×D199 | C2 | semidirect |
| 11. #137×C199 | C2 | semidirect |
| 18. C2×Dic398 | C22 | semidirect |
| 23. Q8×D199 | C22 | semidirect |
| 29. Dic796 | C22 | semidirect |
| 30. #15691876 | C22 | semidirect |
| 31. #15691876 | C22 | semidirect |
| 32. #15691875 | C22 | semidirect |
| 33. #15691874 | C22 | semidirect |
| 34. #15691873 | C22 | semidirect |
| 35. #15691870 | C22 | semidirect |
| 36. #15691869 | C22 | semidirect |
| 39. C2×Q8×C199 | C22 | semidirect |
| 40. Q16×C199 | C22 | semidirect |
| 41. SD16×C199 | C22 | semidirect |
| 42. M16×C199 | C22 | semidirect |
| 98. D199 | #137 | direct (N × H) |
| 99. C199 | C2×#137 | semidirect |
| 108. #137 | D199 | direct (N × H) |
| 125. C2×Q8 | C2×D199 | semidirect |
| 134. Q16 | C2×D199 | semidirect |
| 138. SD16 | C2×D199 | semidirect |
| 141. M16 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D199 | 2 |
| C2×Q8×D199 | 2 |
| #20263988 | 2 |
| #20263987 | 2 |
| #20263986 | 2 |
| #20263985 | 2 |
| #20263984 | 2 |
| Q16×D199 | 2 |
| SD16×D199 | 2 |
| M16×D199 | 2 |
| #137×C199 | 2 |
| C2×#137 | 199 |