Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#16861215 | C2 | semidirect |
| 3. #22550457 | C2 | semidirect |
| 4. #22550135 | C2 | semidirect |
| 5. #22550130 | C2 | semidirect |
| 6. #22550106 | C2 | semidirect |
| 7. #22549875 | C2 | semidirect |
| 8. C2×#106×C127 | C2 | semidirect |
| 55. C2×C8×C127 | D4 | semidirect |
| 106. C127 | #3060 | semidirect |
| 113. C2×#106 | D127 | semidirect |
| 158. C2×C8 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| C2×#16861215 | 2 |
| #22550457 | 2 |
| #22550135 | 2 |
| #22550130 | 2 |
| #22550106 | 2 |
| #22549875 | 2 |
| C2×#106×C127 | 2 |
| #3060 | 127 |