Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22549994 | C2 | semidirect |
| 3. #22549705 | C2 | semidirect |
| 4. #22549683 | C2 | semidirect |
| 5. #22549682 | C2 | semidirect |
| 6. C4×C127⋊C16 | C2 | semidirect |
| 7. #443×C127 | C2 | semidirect |
| 10. #16861155 | C4 | semidirect |
| 11. #16861153 | C4 | semidirect |
| 12. #16861152 | C4 | semidirect |
| 13. #16861150 | C4 | semidirect |
| 72. C127 | #2178 | semidirect |
| 75. #443 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550306 | 2 |
| #22549994 | 2 |
| #22549705 | 2 |
| #22549683 | 2 |
| #22549682 | 2 |
| C4×C127⋊C16 | 2 |
| #443×C127 | 2 |
| #2178 | 127 |