Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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. M16×D199 | C2 | semidirect |
| 3. C42×D199 | C2 | semidirect |
| 4. #20263883 | C2 | semidirect |
| 5. #20263882 | C2 | semidirect |
| 6. #20263881 | C2 | semidirect |
| 7. #104×C199 | C2 | semidirect |
| 8. #15691887 | C4 | semidirect |
| 12. #15691885 | C4 | semidirect |
| 13. Q8×D199 | C4 | semidirect |
| 15. D4×D199 | C4 | semidirect |
| 19. #15691870 | C22 | semidirect |
| 23. C4×Dic199 | C22 | semidirect |
| 25. M16×C199 | C22 | semidirect |
| 26. C42×C199 | C22 | semidirect |
| 30. Dic398 | C2×C4 | semidirect |
| 32. D796 | C2×C4 | semidirect |
| 48. Q8×C199 | C2×C4 | semidirect |
| 50. D4×C199 | C2×C4 | semidirect |
| 75. D199 | #104 | direct (N × H) |
| 76. C199 | C2×#104 | semidirect |
| 84. #104 | D199 | direct (N × H) |
| 99. M16 | C2×D199 | semidirect |
| 103. C42 | C2×D199 | semidirect |
| 108. Q8 | C4×D199 | semidirect |
| 115. D4 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D199 | 2 |
| M16×D199 | 2 |
| C42×D199 | 2 |
| #20263883 | 2 |
| #20263882 | 2 |
| #20263881 | 2 |
| #104×C199 | 2 |
| C2×#104 | 199 |