Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
412 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#16861119 | C2 | semidirect |
| 4. #22549631 | C2 | semidirect |
| 5. #336×C127 | C2 | semidirect |
| 12. (C2×D127)⋊C8 | C4 | semidirect |
| 28. C2×C127⋊C8 | C2×C4 | semidirect |
| 35. C2×C8×C127 | C2×C4 | semidirect |
| 70. C2×D127 | #97 | semidirect |
| 83. C127 | #1749 | semidirect |
| 88. #336 | D127 | semidirect |
| 116. C2×C8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D127 | 2 |
| C2×(C2×D127)⋊C8 | 2 |
| C2×#16861119 | 2 |
| #22549631 | 2 |
| #336×C127 | 2 |
| #1749 | 127 |