Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
400 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 221 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. #22550006 | C2 | direct (N × H) |
| 35. C2×C8×C127 | Q8 | semidirect |
| 56. C8×C127 | C2×Q8 | semidirect |
| 68. C2×C127 | #446 | semidirect |
| 73. C127 | C2×#446 | semidirect |
| 104. C2×C8 | Dic254 | semidirect |
| 129. C8 | C2×Dic254 | semidirect |
| 141. C2 | #22550006 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic254 | 2 |
| #22550006 | 2 |
| C2×C4⋊(C127⋊C8) | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×#16861119 | 2 |
| C2×C4×C8×C127 | 2 |
| C2×#446 | 127 |