Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22549697 | C2 | semidirect |
| 4. #22549653 | C2 | semidirect |
| 5. #364×C127 | C2 | semidirect |
| 53. C127 | #2166 | semidirect |
| 56. #364 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549830 | 2 |
| #22549697 | 2 |
| #22549657 | 2 |
| #22549653 | 2 |
| #364×C127 | 2 |
| #2166 | 127 |