Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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. #21440689 | C2 | semidirect |
| 2. #21440688 | C2 | semidirect |
| 3. #21440675 | C2 | semidirect |
| 4. #21440670 | C2 | semidirect |
| 5. #21440664 | C2 | semidirect |
| 6. C2×#16838759 | C2 | semidirect |
| 7. #131×C241 | C2 | semidirect |
| 10. #16838770 | C22 | semidirect |
| 12. C2×Dic482 | C22 | semidirect |
| 16. Dic964 | C22 | semidirect |
| 17. #16838759 | C22 | semidirect |
| 18. #16838759 | C22 | semidirect |
| 19. #16838759 | C22 | semidirect |
| 20. D1928 | C22 | semidirect |
| 22. M16×C241 | C22 | semidirect |
| 23. C2×C8×C241 | C22 | semidirect |
| 53. C241 | #577 | semidirect |
| 61. #131 | D241 | semidirect |
| 76. M16 | C2×D241 | semidirect |
| 77. C2×C8 | C2×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440689 | 2 |
| #21440688 | 2 |
| #21440675 | 2 |
| #21440670 | 2 |
| #21440664 | 2 |
| C2×#16838759 | 2 |
| #131×C241 | 2 |
| #577 | 241 |