Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. #21440648 | C2 | semidirect |
| 3. #21440577 | C2 | semidirect |
| 4. #21440569 | C2 | semidirect |
| 5. #21440568 | C2 | semidirect |
| 6. #21440552 | C2 | semidirect |
| 7. #131×C241 | C2 | semidirect |
| 9. #16838760 | C4 | semidirect |
| 10. #16838758 | C4 | semidirect |
| 11. #16838757 | C4 | semidirect |
| 12. #16838755 | C4 | semidirect |
| 51. C241 | #444 | semidirect |
| 55. #131 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440662 | 2 |
| #21440648 | 2 |
| #21440577 | 2 |
| #21440569 | 2 |
| #21440568 | 2 |
| #21440552 | 2 |
| #131×C241 | 2 |
| #444 | 241 |