Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #22550281 | C2 | semidirect |
| 3. #22549681 | C2 | semidirect |
| 5. #346×C127 | C2 | semidirect |
| 57. C127 | #2243 | semidirect |
| 62. #346 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550281 | 2 |
| #22550260 | 2 |
| #22549681 | 2 |
| #22549678 | 2 |
| #346×C127 | 2 |
| #2243 | 127 |