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. #21440688 | C2 | semidirect |
| 2. #21440673 | C2 | semidirect |
| 3. #21440667 | C2 | semidirect |
| 4. #21440662 | C2 | semidirect |
| 5. C2×#16838757 | C2 | semidirect |
| 6. #21440649 | C2 | semidirect |
| 7. 2−1+4×C241 | C2 | semidirect |
| 12. #16838760 | C22 | semidirect |
| 13. #16838758 | C22 | semidirect |
| 14. #16838757 | C22 | semidirect |
| 15. #16838757 | C22 | semidirect |
| 16. #16838755 | C22 | semidirect |
| 17. #16838754 | C22 | semidirect |
| 18. C2×#14515349 | C22 | semidirect |
| 21. #41×C241 | C22 | semidirect |
| 23. C2×Q8×C241 | C22 | semidirect |
| 53. C241 | #577 | semidirect |
| 55. 2−1+4 | D241 | semidirect |
| 66. #41 | C2×D241 | semidirect |
| 68. C2×Q8 | C2×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440688 | 2 |
| #21440673 | 2 |
| #21440667 | 2 |
| #21440662 | 2 |
| C2×#16838757 | 2 |
| #21440649 | 2 |
| 2−1+4×C241 | 2 |
| #577 | 241 |