Finite Group DatabasebetaFinite Group DatabasebetaOrder 16064.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D251 | C2 | semidirect |
| 3. #22548714 | C2 | semidirect |
| 4. #22548701 | C2 | semidirect |
| 5. #22548700 | C2 | semidirect |
| 6. #22548697 | C2 | semidirect |
| 7. #22548695 | C2 | semidirect |
| 8. #22548694 | C2 | semidirect |
| 9. #22548691 | C2 | semidirect |
| 10. #22548673 | C2 | semidirect |
| 11. C22⋊Q8×C251 | C2 | semidirect |
| 83. C251 | #536 | semidirect |
| 94. C22⋊Q8 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16860810 | 2 |
| C2×Q8×D251 | 2 |
| #22548714 | 2 |
| #22548701 | 2 |
| #22548700 | 2 |
| #22548697 | 2 |
| #22548695 | 2 |
| #22548694 | 2 |
| #22548691 | 2 |
| #22548673 | 2 |
| C22⋊Q8×C251 | 2 |
| #536 | 251 |