Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #22549783 | C2 | semidirect |
| 5. #22549638 | C2 | semidirect |
| 6. #22549630 | C2 | semidirect |
| 7. C2×#103×C127 | C2 | semidirect |
| 12. C2×#14523235 | C4 | semidirect |
| 42. C2×C127⋊C8 | C2×C4 | semidirect |
| 53. C2×Q8×C127 | C2×C4 | semidirect |
| 81. C2×Dic127 | SD16 | semidirect |
| 134. C127 | #1877 | semidirect |
| 137. C2×#103 | D127 | semidirect |
| 166. C2×Q8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523235 | 2 |
| C2×#16861171 | 2 |
| C2×#16861131 | 2 |
| #22549783 | 2 |
| #22549638 | 2 |
| #22549630 | 2 |
| C2×#103×C127 | 2 |
| #1877 | 127 |