Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
416 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 165 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. #22550159 | C2 | direct (N × H) |
| 48. C2×Q8×C127 | Q8 | semidirect |
| 70. Q8×C127 | C2×Q8 | semidirect |
| 93. C2×C127 | #475 | semidirect |
| 98. C127 | C2×#475 | semidirect |
| 131. C2×Q8 | Dic254 | semidirect |
| 159. Q8 | C2×Dic254 | semidirect |
| 191. C2 | #22550159 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861208 | 2 |
| C2×Q8×Dic127 | 2 |
| #22550159 | 2 |
| C2×#16861141 | 2 |
| C2×#16861140 | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×#16861133 | 2 |
| C2×#103×C127 | 2 |
| C2×#475 | 127 |