Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 13. Dic127⋊C8 | C4 | semidirect |
| 16. C8×Dic127 | C4 | semidirect |
| 53. C127⋊C8 | C4⋊C4 | semidirect |
| 78. Dic127 | #97 | semidirect |
| 85. C127 | #1770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic127⋊C8 | 2 |
| C2×#16861120 | 2 |
| C2×#16861119 | 2 |
| C2×C8×Dic127 | 2 |
| C4×Dic127⋊C4 | 2 |
| #22549630 | 2 |
| #336×C127 | 2 |
| #1770 | 127 |