Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16861241 | C2 | semidirect |
| 2. #22550541 | C2 | semidirect |
| 4. #22550131 | C2 | semidirect |
| 5. #22550083 | C2 | semidirect |
| 6. #22550078 | C2 | semidirect |
| 7. #22550037 | C2 | semidirect |
| 8. #22550030 | C2 | semidirect |
| 9. C4×#14523237 | C2 | semidirect |
| 10. #22549955 | C2 | semidirect |
| 11. #494×C127 | C2 | semidirect |
| 56. #14523237 | D4 | semidirect |
| 122. C4×C127 | #137 | semidirect |
| 135. C127 | #3276 | semidirect |
| 139. #494 | D127 | semidirect |
| 261. C4 | #16861241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861241 | 2 |
| #22550541 | 2 |
| #22550529 | 2 |
| #22550131 | 2 |
| #22550083 | 2 |
| #22550078 | 2 |
| #22550037 | 2 |
| #22550030 | 2 |
| C4×#14523237 | 2 |
| #22549955 | 2 |
| #494×C127 | 2 |
| #3276 | 127 |