Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21440640 | C2 | semidirect |
| 2. #21440637 | C2 | semidirect |
| 3. #21440635 | C2 | semidirect |
| 4. #21440631 | C2 | semidirect |
| 5. #21440628 | C2 | semidirect |
| 6. #21440628 | C2 | semidirect |
| 7. #21440627 | C2 | semidirect |
| 8. #21440625 | C2 | semidirect |
| 9. #21440620 | C2 | semidirect |
| 10. #21440620 | C2 | semidirect |
| 12. #21440607 | C2 | semidirect |
| 13. C4×C22⋊D241 | C2 | semidirect |
| 14. #21440600 | C2 | semidirect |
| 15. C22⋊Q8×C241 | C2 | semidirect |
| 103. C241 | #542 | semidirect |
| 115. C22⋊Q8 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440640 | 2 |
| #21440637 | 2 |
| #21440635 | 2 |
| #21440631 | 2 |
| #21440628 | 2 |
| #21440627 | 2 |
| #21440625 | 2 |
| #21440620 | 2 |
| #21440615 | 2 |
| #21440607 | 2 |
| C4×C22⋊D241 | 2 |
| #21440600 | 2 |
| C22⋊Q8×C241 | 2 |
| #542 | 241 |