Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 173 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×#16861231 | C2 | semidirect |
| 2. #22550426 | C2 | semidirect |
| 3. #22550260 | C2 | semidirect |
| 4. #22550256 | C2 | semidirect |
| 5. #22550253 | C2 | semidirect |
| 6. #22550249 | C2 | semidirect |
| 7. C2×C4×C8×C127 | C2 | semidirect |
| 36. C2×C8×C127 | D4 | semidirect |
| 65. C4×C127 | #135 | semidirect |
| 73. C127 | #3147 | semidirect |
| 80. C2×C4×C8 | D127 | semidirect |
| 107. C2×C8 | D508 | semidirect |
| 139. C4 | #16861231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| #22550426 | 2 |
| #22550260 | 2 |
| #22550256 | 2 |
| #22550253 | 2 |
| #22550249 | 2 |
| C2×C4×C8×C127 | 2 |
| #3147 | 127 |