Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22550005 | C2 | semidirect |
| 3. #22550003 | C2 | semidirect |
| 33. C2×C127⋊C8 | Q8 | semidirect |
| 84. C127 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550429 | 2 |
| #22550005 | 2 |
| #22550003 | 2 |
| #22549902 | 2 |
| #22549899 | 2 |
| #22549834 | 2 |
| #22549832 | 2 |
| C2×#16861119 | 2 |
| #424×C127 | 2 |
| #2961 | 127 |