Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16814666 | C2 | semidirect |
| 2. #20301019 | C2 | semidirect |
| 3. #20301018 | C2 | semidirect |
| 4. #20301014 | C2 | semidirect |
| 5. #20301013 | C2 | semidirect |
| 6. #20301008 | C2 | semidirect |
| 7. C2×#16814650 | C2 | semidirect |
| 8. C2×#41×C229 | C2 | semidirect |
| 12. #16814666 | C22 | semidirect |
| 13. C2×Dic458 | C22 | semidirect |
| 14. C2×D916 | C22 | semidirect |
| 17. #16814656 | C22 | semidirect |
| 18. #16814654 | C22 | semidirect |
| 19. #16814653 | C22 | semidirect |
| 20. #16814651 | C22 | semidirect |
| 21. #16814650 | C22 | semidirect |
| 22. #16814650 | C22 | semidirect |
| 23. C2×#14270080 | C22 | semidirect |
| 27. #41×C229 | C22 | semidirect |
| 28. C2×Q8×C229 | C22 | semidirect |
| 30. C2×D4×C229 | C22 | semidirect |
| 81. C229 | #575 | semidirect |
| 84. C2×#41 | D229 | semidirect |
| 98. #41 | C2×D229 | semidirect |
| 100. C2×Q8 | C2×D229 | semidirect |
| 104. C2×D4 | C2×D229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16814666 | 2 |
| #20301019 | 2 |
| #20301018 | 2 |
| #20301014 | 2 |
| #20301013 | 2 |
| #20301008 | 2 |
| C2×#16814650 | 2 |
| C2×#41×C229 | 2 |
| #575 | 229 |