Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1112 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 621 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. Q8×Dic254 | C2 | direct (N × H) |
| 22. C2×Dic254 | Q8 | direct (N × H) |
| 31. C2×Q8×C127 | Q8 | semidirect |
| 39. Dic254 | C2×Q8 | direct (N × H) |
| 45. Q8×C127 | C2×Q8 | semidirect |
| 61. C2×C127 | Q82 | semidirect |
| 66. C127 | C2×Q82 | semidirect |
| 91. C2×Q8 | Dic254 | direct (N × H) |
| 107. Q8 | C2×Dic254 | direct (N × H) |
| 127. C2 | Q8×Dic254 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic254 | 2 |
| C2×#16861209 | 2 |
| C2×#16861208 | 2 |
| C2×Q8×Dic127 | 2 |
| C2×C4×Dic254 | 2 |
| C2×C4×Q8×C127 | 2 |
| C2×Q82 | 127 |