Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21440637 | C2 | semidirect |
| 2. #21440633 | C2 | semidirect |
| 3. #21440631 | C2 | semidirect |
| 4. #21440626 | C2 | semidirect |
| 6. Q8×Dic241 | C2 | semidirect |
| 7. #21440604 | C2 | semidirect |
| 8. #21440602 | C2 | semidirect |
| 9. #21440600 | C2 | semidirect |
| 10. C2×C4×Dic241 | C2 | semidirect |
| 11. C22⋊Q8×C241 | C2 | semidirect |
| 74. C241 | #529 | semidirect |
| 80. C22⋊Q8 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440637 | 2 |
| #21440633 | 2 |
| #21440631 | 2 |
| #21440626 | 2 |
| #21440616 | 2 |
| Q8×Dic241 | 2 |
| #21440604 | 2 |
| #21440602 | 2 |
| #21440600 | 2 |
| C2×C4×Dic241 | 2 |
| C22⋊Q8×C241 | 2 |
| #529 | 241 |