Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. #22549700 | C2 | semidirect |
| 3. #22549691 | C2 | semidirect |
| 52. C127 | #2239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550134 | 2 |
| #22549700 | 2 |
| #22549691 | 2 |
| #22549658 | 2 |
| #430×C127 | 2 |
| #2239 | 127 |