Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 80. C127 | #2090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549918 | 2 |
| #22549916 | 2 |
| C2×#16861140 | 2 |
| #22549904 | 2 |
| #22549644 | 2 |
| #22549640 | 2 |
| #343×C127 | 2 |
| #2090 | 127 |