Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22550433 | C2 | semidirect |
| 3. #22550241 | C2 | semidirect |
| 4. #22550223 | C2 | semidirect |
| 5. #22549882 | C2 | semidirect |
| 6. C4×M16×C127 | C2 | semidirect |
| 9. #16861209 | C22 | semidirect |
| 13. #16861201 | C22 | semidirect |
| 17. #16861131 | C22 | semidirect |
| 20. #97×C127 | C22 | semidirect |
| 21. C4×C8×C127 | C22 | semidirect |
| 75. C127 | #3138 | semidirect |
| 81. C4×M16 | D127 | semidirect |
| 95. #97 | C2×D127 | semidirect |
| 96. C4×C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550433 | 2 |
| C2×#16861206 | 2 |
| #22550241 | 2 |
| #22550223 | 2 |
| #22549882 | 2 |
| C4×M16×C127 | 2 |
| #3138 | 127 |