Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16812732 | C2 | semidirect |
| 2. C2×#16812727 | C2 | semidirect |
| 3. C2×#16812721 | C2 | semidirect |
| 4. C22×#13182018 | C2 | semidirect |
| 5. #20295602 | C2 | semidirect |
| 6. #20295595 | C2 | semidirect |
| 7. #20295420 | C2 | semidirect |
| 8. #20295415 | C2 | semidirect |
| 9. #20295410 | C2 | semidirect |
| 10. #20295399 | C2 | semidirect |
| 11. #405×C109 | C2 | semidirect |
| 19. C2×Dic436 | C22 | semidirect |
| 20. C2×Dic436 | C22 | semidirect |
| 25. C2×#13182018 | C22 | semidirect |
| 26. C2×#13182018 | C22 | semidirect |
| 27. C2×#13182018 | C22 | semidirect |
| 29. C2×D872 | C22 | semidirect |
| 30. #16812699 | C22 | semidirect |
| 33. #16812687 | C22 | semidirect |
| 41. #97×C109 | C22 | semidirect |
| 42. C4×C8×C109 | C22 | semidirect |
| 80. M16×C109 | D4 | semidirect |
| 81. C2×C8×C109 | D4 | semidirect |
| 149. C109 | #3154 | semidirect |
| 160. #405 | D109 | semidirect |
| 190. #97 | C2×D109 | semidirect |
| 191. C4×C8 | C2×D109 | semidirect |
| 226. M16 | D436 | semidirect |
| 227. C2×C8 | D436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812732 | 2 |
| C2×#16812727 | 2 |
| C2×#16812721 | 2 |
| C22×#13182018 | 2 |
| #20295602 | 2 |
| #20295595 | 2 |
| #20295420 | 2 |
| #20295415 | 2 |
| #20295410 | 2 |
| #20295399 | 2 |
| #405×C109 | 2 |
| #3154 | 109 |