Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22550274 | C2 | semidirect |
| 4. #22550249 | C2 | semidirect |
| 5. #22550227 | C2 | semidirect |
| 6. #22550223 | C2 | semidirect |
| 7. #22550105 | C2 | semidirect |
| 8. C4×#14523237 | C2 | semidirect |
| 9. C2×C4×C8×C127 | C2 | semidirect |
| 82. C2×C4×C127 | SD16 | semidirect |
| 90. C8×C127 | #41 | semidirect |
| 113. C127 | #3167 | semidirect |
| 122. C2×C4×C8 | D127 | semidirect |
| 195. C2×C4 | #14523237 | semidirect |
| 203. C8 | #14523248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550433 | 2 |
| #22550426 | 2 |
| #22550274 | 2 |
| #22550249 | 2 |
| #22550227 | 2 |
| #22550223 | 2 |
| #22550105 | 2 |
| C4×#14523237 | 2 |
| C2×C4×C8×C127 | 2 |
| #3167 | 127 |