Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
166 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. #22550000 | C2 | semidirect |
| 4. #22549606 | C2 | semidirect |
| 6. #22549598 | C2 | semidirect |
| 7. #335×C127 | C2 | semidirect |
| 43. Dic254 | M16 | semidirect |
| 78. C127 | #1588 | semidirect |
| 82. #335 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550000 | 2 |
| C4×#14523237 | 2 |
| #22549953 | 2 |
| #22549606 | 2 |
| #22549603 | 2 |
| #22549598 | 2 |
| #335×C127 | 2 |
| #1588 | 127 |