Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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. C4×C4⋊Dic127 | C2 | semidirect |
| 3. #22549723 | C2 | semidirect |
| 4. #95×D127 | C2 | semidirect |
| 5. #376×C127 | C2 | semidirect |
| 8. C4×D508 | C4 | semidirect |
| 20. C2×C4×D127 | C2×C4 | semidirect |
| 21. C4⋊Dic127 | C2×C4 | semidirect |
| 22. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 27. C42×C127 | C2×C4 | semidirect |
| 31. D508 | C42 | semidirect |
| 57. C127 | #2275 | semidirect |
| 61. #376 | D127 | semidirect |
| 84. C42 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D508 | 2 |
| C4×C4⋊Dic127 | 2 |
| #22549723 | 2 |
| #95×D127 | 2 |
| #376×C127 | 2 |
| #2275 | 127 |