Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20295680 | C2 | semidirect |
| 2. #20295372 | C2 | semidirect |
| 3. #20295337 | C2 | semidirect |
| 4. #20295306 | C2 | semidirect |
| 5. #20295260 | C2 | semidirect |
| 6. #20295218 | C2 | semidirect |
| 7. #20295160 | C2 | semidirect |
| 8. C4×#13182014 | C2 | semidirect |
| 9. D4×#11724784 | C2 | semidirect |
| 10. C2×#16812620 | C2 | semidirect |
| 11. D42×C109 | C2 | semidirect |
| 14. C2×#13182014 | C22 | semidirect |
| 15. C22×#11724784 | C22 | semidirect |
| 16. #16812699 | C22 | semidirect |
| 19. #16812673 | C22 | semidirect |
| 20. C4×D436 | C22 | semidirect |
| 21. C2×C4⋊Dic109 | C22 | semidirect |
| 22. #16812632 | C22 | semidirect |
| 23. #16812632 | C22 | semidirect |
| 24. C4⋊#11724784 | C22 | semidirect |
| 27. #16812620 | C22 | semidirect |
| 28. #16812620 | C22 | semidirect |
| 29. #16812620 | C22 | semidirect |
| 30. #16812619 | C22 | semidirect |
| 31. C22⋊#11724784 | C22 | semidirect |
| 32. C4×#11724784 | C22 | semidirect |
| 92. D4×C109 | D8 | semidirect |
| 93. D4×C109 | #41 | semidirect |
| 143. C109 | #3294 | semidirect |
| 145. D42 | D109 | semidirect |
| 239. D4 | #13182014 | semidirect |
| 240. D4 | #13182028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295680 | 2 |
| #20295372 | 2 |
| #20295337 | 2 |
| #20295306 | 2 |
| #20295260 | 2 |
| #20295218 | 2 |
| #20295160 | 2 |
| C4×#13182014 | 2 |
| D4×#11724784 | 2 |
| C2×#16812620 | 2 |
| D42×C109 | 2 |
| #3294 | 109 |