Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22549993 | C2 | semidirect |
| 3. #22549992 | C2 | semidirect |
| 4. #22549705 | C2 | semidirect |
| 5. #22549684 | C2 | semidirect |
| 6. C16×Dic127 | C2 | semidirect |
| 7. #359×C127 | C2 | semidirect |
| 11. #16861155 | C4 | semidirect |
| 12. #16861153 | C4 | semidirect |
| 13. #16861152 | C4 | semidirect |
| 14. #16861150 | C4 | semidirect |
| 72. C127 | #2178 | semidirect |
| 78. #359 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550306 | 2 |
| #22549993 | 2 |
| #22549992 | 2 |
| #22549705 | 2 |
| #22549684 | 2 |
| C16×Dic127 | 2 |
| #359×C127 | 2 |
| #2178 | 127 |