Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
280 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 280 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 |
|---|---|---|
| 10. #16861142 | C4 | semidirect |
| 11. C8×Dic127 | C4 | semidirect |
| 39. C127⋊C8 | C42 | semidirect |
| 60. Dic127 | #107 | semidirect |
| 67. C127 | C4×#107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861142 | 2 |
| C2×C8×Dic127 | 2 |
| C4⋊C4×Dic127 | 2 |
| #22549639 | 2 |
| #340×C127 | 2 |
| C4×#107 | 127 |