Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×D199 | C2 | semidirect |
| 3. #20263935 | C2 | semidirect |
| 4. #20263934 | C2 | semidirect |
| 5. #20263933 | C2 | semidirect |
| 6. #20263932 | C2 | semidirect |
| 7. #20263931 | C2 | semidirect |
| 8. C4⋊C4×D199 | C2 | semidirect |
| 9. C4⋊C4×D199 | C2 | semidirect |
| 11. C22⋊Q8×C199 | C2 | semidirect |
| 13. C2×Dic398 | C22 | semidirect |
| 14. C2×Dic398 | C22 | semidirect |
| 24. C4⋊Dic199 | C22 | semidirect |
| 25. C4⋊Dic199 | C22 | semidirect |
| 26. Dic199⋊C4 | C22 | semidirect |
| 27. Dic199⋊C4 | C22 | semidirect |
| 28. Dic199⋊C4 | C22 | semidirect |
| 32. C2×Q8×C199 | C22 | semidirect |
| 34. C4⋊C4×C199 | C22 | semidirect |
| 35. C4⋊C4×C199 | C22 | semidirect |
| 39. C22×D199 | Q8 | semidirect |
| 64. C22×C199 | C2×Q8 | semidirect |
| 71. C2×D199 | C2×Q8 | semidirect |
| 86. D199 | C22⋊Q8 | direct (N × H) |
| 87. C199 | C2×C22⋊Q8 | semidirect |
| 96. C22⋊Q8 | D199 | direct (N × H) |
| 104. C2×Q8 | C2×D199 | semidirect |
| 119. C4⋊C4 | C2×D199 | semidirect |
| 120. C4⋊C4 | C2×D199 | semidirect |
| 159. C22 | Q8×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D199 | 2 |
| C22×C4×D199 | 2 |
| #20263935 | 2 |
| #20263934 | 2 |
| #20263933 | 2 |
| #20263932 | 2 |
| #20263931 | 2 |
| C4⋊C4×D199 | 2 |
| C22⋊C4×D199 | 2 |
| C22⋊Q8×C199 | 2 |
| C2×C22⋊Q8 | 199 |