Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
400 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 54. C127 | #2402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549818 | 2 |
| #22549810 | 2 |
| C4×Dic127⋊C4 | 2 |
| C4×C4⋊Dic127 | 2 |
| #376×C127 | 2 |
| #2402 | 127 |