Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 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. #22550354 | C2 | semidirect |
| 3. #22550353 | C2 | semidirect |
| 4. #22550352 | C2 | semidirect |
| 5. C4×Q8×D127 | C2 | semidirect |
| 7. #519×C127 | C2 | semidirect |
| 9. C2×Q8×D127 | C4 | semidirect |
| 13. Q8×Dic127 | C22 | semidirect |
| 14. C4×Dic254 | C22 | semidirect |
| 15. #16861174 | C22 | semidirect |
| 24. C4×Q8×C127 | C22 | semidirect |
| 27. C2×Dic254 | C2×C4 | semidirect |
| 30. Q8×D127 | C2×C4 | semidirect |
| 42. C2×Q8×C127 | C2×C4 | semidirect |
| 80. D127 | #519 | direct (N × H) |
| 82. C127 | C2×#519 | semidirect |
| 87. #519 | D127 | direct (N × H) |
| 99. C4×Q8 | C2×D127 | semidirect |
| 113. 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×Q8×D127 | 2 |
| #22550354 | 2 |
| #22550353 | 2 |
| #22550352 | 2 |
| C4×Q8×D127 | 2 |
| #117×D127 | 2 |
| #519×C127 | 2 |
| C2×#519 | 127 |