Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22549925 | C2 | semidirect |
| 4. M16×Dic127 | C2 | semidirect |
| 5. #22549648 | C2 | semidirect |
| 6. #22549637 | C2 | semidirect |
| 21. #101×C127 | C4 | semidirect |
| 22. #100×C127 | C4 | semidirect |
| 96. C127 | #1932 | semidirect |
| 115. #101 | Dic127 | semidirect |
| 116. #100 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549925 | 2 |
| #22549893 | 2 |
| C2×#16861136 | 2 |
| M16×Dic127 | 2 |
| #22549648 | 2 |
| #22549637 | 2 |
| #413×C127 | 2 |
| #1932 | 127 |