Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #22549984 | C2 | semidirect |
| 4. #22549983 | C2 | semidirect |
| 5. #22549982 | C2 | semidirect |
| 6. C4×#14523238 | C2 | semidirect |
| 7. #22549968 | C2 | semidirect |
| 11. #441×C127 | C2 | semidirect |
| 15. Q16×D127 | C4 | semidirect |
| 109. C127 | #2950 | semidirect |
| 115. #441 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D127 | 2 |
| #22550352 | 2 |
| #22549984 | 2 |
| #22549983 | 2 |
| #22549982 | 2 |
| C4×#14523238 | 2 |
| #22549968 | 2 |
| #22549911 | 2 |
| #22549883 | 2 |
| #22549833 | 2 |
| #441×C127 | 2 |
| #2950 | 127 |