Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#16861217 | C2 | semidirect |
| 2. C22×#14523231 | C2 | semidirect |
| 4. #22549953 | C2 | semidirect |
| 5. #22549946 | C2 | semidirect |
| 6. #22549842 | C2 | semidirect |
| 7. #22549839 | C2 | semidirect |
| 8. #22549832 | C2 | semidirect |
| 9. #424×C127 | C2 | semidirect |
| 17. C2×#14523231 | C22 | semidirect |
| 19. C2×C8×D127 | C22 | semidirect |
| 26. (C2×D127)⋊C8 | C22 | semidirect |
| 27. #16861120 | C22 | semidirect |
| 28. C4×C127⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C127 | C22 | semidirect |
| 50. C2×C127⋊C8 | D4 | semidirect |
| 114. C127 | #2930 | semidirect |
| 120. #424 | D127 | semidirect |
| 142. C4⋊C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861217 | 2 |
| C22×#14523231 | 2 |
| #22550388 | 2 |
| #22549953 | 2 |
| #22549946 | 2 |
| #22549842 | 2 |
| #22549839 | 2 |
| #22549832 | 2 |
| #424×C127 | 2 |
| #2930 | 127 |