Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1088 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 341 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×#16861168 | C2 | semidirect |
| 2. #22549739 | C2 | semidirect |
| 3. #22549736 | C2 | semidirect |
| 5. C4×C22⋊Dic127 | C2 | semidirect |
| 8. C2×C4⋊Dic127 | C22 | semidirect |
| 11. C2×C4×Dic127 | C22 | semidirect |
| 12. C127⋊#95 | C22 | semidirect |
| 15. C23×C4×C127 | C4 | semidirect |
| 59. C2×C4×C127 | C22⋊C4 | semidirect |
| 72. C22×C127 | #117 | semidirect |
| 86. C127 | #2280 | semidirect |
| 95. C23×C4 | Dic127 | semidirect |
| 145. C2×C4 | C22⋊Dic127 | semidirect |
| 158. C22 | #16861168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861168 | 2 |
| #22549739 | 2 |
| #22549736 | 2 |
| #22549732 | 2 |
| C4×C22⋊Dic127 | 2 |
| C24×C4×C127 | 2 |
| #2280 | 127 |