Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×#16861144 | C2 | semidirect |
| 5. #22549635 | C2 | semidirect |
| 6. #22549630 | C2 | semidirect |
| 7. #405×C127 | C2 | semidirect |
| 14. #16861132 | C4 | semidirect |
| 15. #16861132 | C4 | semidirect |
| 16. #16861129 | C4 | semidirect |
| 17. #16861129 | C4 | semidirect |
| 106. C127 | #1929 | semidirect |
| 111. #405 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861144 | 2 |
| C2×#16861135 | 2 |
| #22549870 | 2 |
| #22549842 | 2 |
| #22549635 | 2 |
| #22549630 | 2 |
| #405×C127 | 2 |
| #1929 | 127 |