Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
236 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 84. C127 | #1830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550353 | 2 |
| C2×#16861127 | 2 |
| #22549648 | 2 |
| #22549647 | 2 |
| #22549646 | 2 |
| #344×C127 | 2 |
| #1830 | 127 |