Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 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×C4⋊(C127⋊C8) | C2 | semidirect |
| 3. #22549608 | C2 | semidirect |
| 4. #22549605 | C2 | semidirect |
| 5. #431×C127 | C2 | semidirect |
| 24. #14523248 | C8 | semidirect |
| 53. Dic254 | C2×C8 | semidirect |
| 55. D508 | C2×C8 | semidirect |
| 102. C127 | #1477 | semidirect |
| 104. #431 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523248 | 2 |
| C2×C4⋊(C127⋊C8) | 2 |
| #22549608 | 2 |
| #22549605 | 2 |
| #431×C127 | 2 |
| #1477 | 127 |