Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
280 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 280 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 |
|---|---|---|
| 9. C4×C127⋊C8 | C4 | semidirect |
| 28. C127⋊C8 | C4⋊C4 | semidirect |
| 45. C4×C127 | #107 | semidirect |
| 55. C127 | #1845 | semidirect |
| 101. C4 | #16861142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861142 | 2 |
| C2×C4×C127⋊C8 | 2 |
| #22549746 | 2 |
| #384×C127 | 2 |
| #1845 | 127 |