Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
908 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 277 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. #22549796 | C2 | direct (N × H) |
| 29. C22×Dic127 | Q8 | semidirect |
| 40. C22×C4×C127 | Q8 | semidirect |
| 53. C2×Dic127 | C2×Q8 | semidirect |
| 69. C2×C4×C127 | C2×Q8 | semidirect |
| 85. C2×C127 | #395 | semidirect |
| 92. C127 | C2×#395 | semidirect |
| 131. C22×C4 | Dic254 | semidirect |
| 161. C2×C4 | C2×Dic254 | semidirect |
| 177. C2 | #22549796 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic254 | 2 |
| C22×Dic127⋊C4 | 2 |
| #22549796 | 2 |
| C2×C127⋊#95 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C2×#395 | 127 |