Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#16861232 | C2 | semidirect |
| 2. #22550529 | C2 | semidirect |
| 3. #22550114 | C2 | semidirect |
| 4. #22550078 | C2 | semidirect |
| 5. #22550037 | C2 | semidirect |
| 6. C4×D1016 | C2 | semidirect |
| 7. C8×D508 | C2 | semidirect |
| 8. #494×C127 | C2 | semidirect |
| 38. D1016 | D4 | semidirect |
| 85. C4×C127 | #135 | semidirect |
| 96. C127 | #3283 | semidirect |
| 99. #494 | D127 | semidirect |
| 183. C4 | #16861232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861232 | 2 |
| #22550529 | 2 |
| #22550114 | 2 |
| #22550078 | 2 |
| #22550037 | 2 |
| C4×D1016 | 2 |
| C8×D508 | 2 |
| #494×C127 | 2 |
| #3283 | 127 |