Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
276 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22549606 | C2 | semidirect |
| 4. #22549603 | C2 | semidirect |
| 5. #431×C127 | C2 | semidirect |
| 24. #14523248 | C8 | semidirect |
| 53. Dic254 | C2×C8 | semidirect |
| 55. D508 | C2×C8 | semidirect |
| 99. C127 | #1476 | semidirect |
| 101. #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 |
| #22549606 | 2 |
| #22549603 | 2 |
| #431×C127 | 2 |
| #1476 | 127 |