Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
820 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 3. #22549802 | C2 | direct (N × H) |
| 4. C2×C127⋊#95 | C2 | semidirect |
| 5. C2×C127⋊#95 | C2 | semidirect |
| 6. C22×C4⋊C4×C127 | C2 | semidirect |
| 14. C127⋊#95 | C22 | semidirect |
| 15. C127⋊#95 | C22 | semidirect |
| 19. C2×C4⋊C4×C127 | C22 | semidirect |
| 94. C2×C127 | #397 | semidirect |
| 102. C127 | C2×#397 | semidirect |
| 103. C22×C4⋊C4 | D127 | semidirect |
| 115. C2×C4⋊C4 | C2×D127 | semidirect |
| 197. C2 | #22549802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D127)⋊C4 | 2 |
| #22549802 | 2 |
| C2×C127⋊#95 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C2×#397 | 127 |