Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22549936 | C2 | semidirect |
| 3. #22549900 | C2 | semidirect |
| 5. M16×Dic127 | C2 | semidirect |
| 6. #423×C127 | C2 | semidirect |
| 14. C4⋊(C127⋊C8) | C22 | semidirect |
| 16. #16861119 | C22 | semidirect |
| 17. C8×Dic127 | C22 | semidirect |
| 20. C4⋊C8×C127 | C22 | semidirect |
| 76. C127 | #2921 | semidirect |
| 80. #423 | D127 | semidirect |
| 93. C4⋊C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861166 | 2 |
| #22549936 | 2 |
| #22549900 | 2 |
| #22549839 | 2 |
| M16×Dic127 | 2 |
| #423×C127 | 2 |
| #2921 | 127 |