Finite Group DatabasebetaFinite Group DatabasebetaOrder 16064.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22548763 | C2 | semidirect |
| 2. #22548762 | C2 | semidirect |
| 3. #22548748 | C2 | semidirect |
| 4. #22548747 | C2 | semidirect |
| 5. #22548744 | C2 | semidirect |
| 6. #22548736 | C2 | semidirect |
| 7. #22548735 | C2 | semidirect |
| 8. C2×#16860800 | C2 | semidirect |
| 9. Q16×D251 | C2 | semidirect |
| 10. #22548723 | C2 | semidirect |
| 11. #137×C251 | C2 | semidirect |
| 87. C251 | #578 | semidirect |
| 94. #137 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22548763 | 2 |
| #22548762 | 2 |
| #22548748 | 2 |
| #22548747 | 2 |
| #22548744 | 2 |
| #22548736 | 2 |
| #22548735 | 2 |
| C2×#16860800 | 2 |
| Q16×D251 | 2 |
| #22548723 | 2 |
| #137×C251 | 2 |
| #578 | 251 |