Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×Dic127⋊C8 | C2 | semidirect |
| 5. #22549631 | C2 | semidirect |
| 6. #22549630 | C2 | semidirect |
| 7. C2×C4⋊C8×C127 | C2 | semidirect |
| 43. (C2×D127)⋊C4 | C8 | semidirect |
| 72. C2×Dic127 | C2×C8 | semidirect |
| 85. C2×C4×C127 | C2×C8 | semidirect |
| 107. C2×D127 | C4⋊C8 | semidirect |
| 126. C127 | #1850 | semidirect |
| 129. C2×C4⋊C8 | D127 | semidirect |
| 209. C2×C4 | C8×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D127 | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×(C2×D127)⋊C8 | 2 |
| C4×(C2×D127)⋊C4 | 2 |
| #22549631 | 2 |
| #22549630 | 2 |
| C2×C4⋊C8×C127 | 2 |
| #1850 | 127 |