Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×#14523232 | C2 | semidirect |
| 4. #22549636 | C2 | semidirect |
| 5. C43×C127 | C2 | semidirect |
| 8. C4×Dic254 | C4 | semidirect |
| 9. C4×D508 | C4 | semidirect |
| 14. #16861137 | C4 | direct (N × H) |
| 28. #14523232 | C2×C4 | semidirect |
| 42. C42×C127 | C2×C4 | semidirect |
| 47. Dic254 | C42 | semidirect |
| 49. D508 | C42 | semidirect |
| 73. C4×C127 | #104 | semidirect |
| 84. C127 | C4×#104 | semidirect |
| 88. C43 | D127 | semidirect |
| 126. C42 | C4×D127 | semidirect |
| 159. C4 | #16861137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523248 | 2 |
| C2×#16861137 | 2 |
| C4×#14523232 | 2 |
| #22549636 | 2 |
| C43×C127 | 2 |
| C4×#104 | 127 |