Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22550272 | C2 | semidirect |
| 3. #22550227 | C2 | semidirect |
| 4. #22550226 | C2 | semidirect |
| 6. C8×C127⋊C8 | C2 | semidirect |
| 69. C127 | #1708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550272 | 2 |
| #22550248 | 2 |
| #22550227 | 2 |
| #22550226 | 2 |
| #22550222 | 2 |
| C8×C127⋊C8 | 2 |
| #486×C127 | 2 |
| #1708 | 127 |