Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
176 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 6. C4⋊(C127⋊C8) | C4 | semidirect |
| 13. C4⋊C8×C127 | C4 | semidirect |
| 67. C127 | #1303 | semidirect |
| 77. C4⋊C8 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549929 | 2 |
| C4×C4⋊Dic127 | 2 |
| #423×C127 | 2 |
| #1303 | 127 |