Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22549875 | C2 | semidirect |
| 4. C2×#16861129 | C2 | semidirect |
| 5. C2×#16861125 | C2 | semidirect |
| 6. #22549844 | C2 | semidirect |
| 7. #343×C127 | C2 | semidirect |
| 117. C127 | #2051 | semidirect |
| 124. #343 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861237 | 2 |
| C2×#16861144 | 2 |
| #22549875 | 2 |
| C2×#16861129 | 2 |
| C2×#16861125 | 2 |
| #22549844 | 2 |
| #343×C127 | 2 |
| #2051 | 127 |