Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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×#16861148 | C2 | semidirect |
| 3. #107×D127 | C2 | semidirect |
| 4. #22549680 | C2 | semidirect |
| 5. #22549678 | C2 | semidirect |
| 6. #22549676 | C2 | semidirect |
| 7. #358×C127 | C2 | semidirect |
| 10. #16861232 | C4 | semidirect |
| 31. D1016 | C2×C4 | semidirect |
| 40. Q16×C127 | C2×C4 | semidirect |
| 82. C127 | #2139 | semidirect |
| 87. #358 | D127 | semidirect |
| 113. Q16 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861232 | 2 |
| C2×#16861148 | 2 |
| #107×D127 | 2 |
| #22549680 | 2 |
| #22549678 | 2 |
| #22549676 | 2 |
| #358×C127 | 2 |
| #2139 | 127 |