Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 10. Q8×Dic127 | C4 | semidirect |
| 17. #16861133 | C4 | semidirect |
| 23. #103×C127 | C4 | semidirect |
| 71. Q8×C127 | C42 | semidirect |
| 110. C127 | #1763 | semidirect |
| 131. #103 | Dic127 | semidirect |
| 168. Q8 | C4×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic127 | 2 |
| C2×#16861133 | 2 |
| C2×#16861119 | 2 |
| C4⋊C4×Dic127 | 2 |
| #22549639 | 2 |
| #22549638 | 2 |
| C2×#103×C127 | 2 |
| #1763 | 127 |