Finite Group DatabasebetaFinite Group DatabasebetaOrder 16064.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 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. #22548710 | C2 | semidirect |
| 2. #22548706 | C2 | semidirect |
| 3. #22548705 | C2 | semidirect |
| 5. #22548695 | C2 | semidirect |
| 6. #22548694 | C2 | semidirect |
| 7. #22548680 | C2 | semidirect |
| 9. #22548674 | C2 | semidirect |
| 10. #22548673 | C2 | semidirect |
| 11. C2×C4⋊C4×C251 | C2 | semidirect |
| 72. C251 | #552 | semidirect |
| 84. C2×C4⋊C4 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22548710 | 2 |
| #22548706 | 2 |
| #22548705 | 2 |
| #22548698 | 2 |
| #22548695 | 2 |
| #22548694 | 2 |
| #22548680 | 2 |
| C4×C22⋊D251 | 2 |
| #22548674 | 2 |
| #22548673 | 2 |
| C2×C4⋊C4×C251 | 2 |
| #552 | 251 |