Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
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×#16838770 | C2 | semidirect |
| 2. #21440673 | C2 | semidirect |
| 3. #21440672 | C2 | semidirect |
| 4. #21440668 | C2 | semidirect |
| 5. #21440667 | C2 | semidirect |
| 6. #21440662 | C2 | semidirect |
| 7. C2×#16838754 | C2 | semidirect |
| 8. C2×#41×C241 | C2 | semidirect |
| 12. #16838770 | C22 | semidirect |
| 13. C2×Dic482 | C22 | semidirect |
| 14. C2×D964 | C22 | semidirect |
| 17. #16838760 | C22 | semidirect |
| 18. #16838758 | C22 | semidirect |
| 19. #16838757 | C22 | semidirect |
| 20. #16838755 | C22 | semidirect |
| 21. #16838754 | C22 | semidirect |
| 22. #16838754 | C22 | semidirect |
| 23. C2×#14515349 | C22 | semidirect |
| 27. #41×C241 | C22 | semidirect |
| 28. C2×Q8×C241 | C22 | semidirect |
| 30. C2×D4×C241 | C22 | semidirect |
| 81. C241 | #575 | semidirect |
| 84. C2×#41 | D241 | semidirect |
| 98. #41 | C2×D241 | semidirect |
| 100. C2×Q8 | C2×D241 | semidirect |
| 104. C2×D4 | C2×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838770 | 2 |
| #21440673 | 2 |
| #21440672 | 2 |
| #21440668 | 2 |
| #21440667 | 2 |
| #21440662 | 2 |
| C2×#16838754 | 2 |
| C2×#41×C241 | 2 |
| #575 | 241 |