Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
192 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. C8×D508 | C2 | semidirect |
| 3. #22549626 | C2 | semidirect |
| 4. D4⋊(C127⋊C8) | C2 | semidirect |
| 5. #22549603 | C2 | semidirect |
| 6. #22549598 | C2 | semidirect |
| 7. C8×D4×C127 | C2 | semidirect |
| 25. #14523233 | C8 | semidirect |
| 44. D508 | C2×C8 | semidirect |
| 51. C127⋊C8 | C2×C8 | semidirect |
| 54. D4×C127 | C2×C8 | semidirect |
| 84. C127 | #1580 | semidirect |
| 87. C8×D4 | D127 | semidirect |
| 131. D4 | C8×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523233 | 2 |
| C8×D508 | 2 |
| #22549626 | 2 |
| D4⋊(C127⋊C8) | 2 |
| #22549603 | 2 |
| #22549598 | 2 |
| C8×D4×C127 | 2 |
| #1580 | 127 |