Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22549924 | C2 | semidirect |
| 5. M16×Dic127 | C2 | semidirect |
| 6. #22549635 | C2 | semidirect |
| 7. #344×C127 | C2 | semidirect |
| 16. #16861127 | C4 | semidirect |
| 17. #16861125 | C4 | semidirect |
| 96. C127 | #1932 | semidirect |
| 102. #344 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549924 | 2 |
| #22549894 | 2 |
| C2×#16861135 | 2 |
| #22549858 | 2 |
| M16×Dic127 | 2 |
| #22549635 | 2 |
| #344×C127 | 2 |
| #1932 | 127 |