Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
280 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 280 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 |
|---|---|---|
| 12. C8×Dic127 | C4 | semidirect |
| 37. C127⋊C8 | C4⋊C4 | semidirect |
| 47. C8×C127 | C4⋊C4 | semidirect |
| 58. Dic127 | #106 | semidirect |
| 64. C127 | #1844 | semidirect |
| 111. C8 | Dic127⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861141 | 2 |
| C2×#16861140 | 2 |
| C2×C8×Dic127 | 2 |
| #22549745 | 2 |
| C2×#106×C127 | 2 |
| #1844 | 127 |