Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#16861144 | C2 | semidirect |
| 3. C2×#16861142 | C2 | semidirect |
| 6. #22549644 | C2 | semidirect |
| 7. #343×C127 | C2 | semidirect |
| 10. #16861217 | C4 | semidirect |
| 104. C127 | #1816 | semidirect |
| 111. #343 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861217 | 2 |
| C2×#16861144 | 2 |
| C2×#16861142 | 2 |
| #22549878 | 2 |
| #22549875 | 2 |
| #22549644 | 2 |
| #343×C127 | 2 |
| #1816 | 127 |