Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
576 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 285 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. #22549899 | C2 | direct (N × H) |
| 4. C2×Dic127⋊C8 | C2 | semidirect |
| 15. Dic127⋊C8 | C22 | semidirect |
| 43. C2×Dic127 | M16 | semidirect |
| 72. Dic127 | C2×M16 | semidirect |
| 74. C2×C127 | #423 | semidirect |
| 78. C127 | C2×#423 | semidirect |
| 152. C2 | #22549899 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523232 | 2 |
| C22×C4×Dic127 | 2 |
| #22549899 | 2 |
| C2×Dic127⋊C8 | 2 |
| C22×M16×C127 | 2 |
| C2×#423 | 127 |