Finite Group DatabasebetaFinite Group DatabasebetaOrder 16064.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×#16860797 | C2 | semidirect |
| 2. C2×#16860794 | C2 | semidirect |
| 4. #22548648 | C2 | semidirect |
| 5. #22548639 | C2 | semidirect |
| 6. #22548635 | C2 | semidirect |
| 7. C22⋊Q8×C251 | C2 | semidirect |
| 27. C251⋊C8 | D4 | semidirect |
| 55. C251 | #468 | semidirect |
| 59. C22⋊Q8 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16860797 | 2 |
| C2×#16860794 | 2 |
| #22548689 | 2 |
| #22548648 | 2 |
| #22548639 | 2 |
| #22548635 | 2 |
| C22⋊Q8×C251 | 2 |
| #468 | 251 |