Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 565 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. #22550507 | C2 | direct (N × H) |
| 2. C2×#16861208 | C2 | semidirect |
| 3. C2×#16861200 | C2 | semidirect |
| 8. #16861208 | C22 | semidirect |
| 9. #16861200 | C22 | semidirect |
| 34. C22×C4×C127 | Q8 | semidirect |
| 53. C2×C4×C127 | C2×Q8 | semidirect |
| 69. C2×C127 | #544 | semidirect |
| 74. C127 | C2×#544 | semidirect |
| 102. C22×C4 | Dic254 | semidirect |
| 127. C2×C4 | C2×Dic254 | semidirect |
| 143. C2 | #22550507 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550507 | 2 |
| C2×#16861208 | 2 |
| C2×#16861200 | 2 |
| C2×#16861188 | 2 |
| C2×#16861168 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C2×#544 | 127 |