Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
936 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 936 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 |
|---|---|---|
| 2. C2×#16861168 | C2 | semidirect |
| 3. #22549782 | C2 | semidirect |
| 4. #22549778 | C2 | semidirect |
| 5. #22549755 | C2 | semidirect |
| 6. C4×(C2×D127)⋊C4 | C2 | semidirect |
| 7. C22×C42×C127 | C2 | semidirect |
| 10. C2×#14523248 | C4 | semidirect |
| 30. C2×Dic254 | C2×C4 | semidirect |
| 33. C2×D508 | C2×C4 | semidirect |
| 41. C2×C4×D127 | C2×C4 | semidirect |
| 78. C2×C4×C127 | C22⋊C4 | semidirect |
| 85. C2×C4×C127 | #41 | semidirect |
| 110. C127 | #2297 | semidirect |
| 113. C22×C42 | D127 | semidirect |
| 188. C2×C4 | (C2×D127)⋊C4 | semidirect |
| 195. C2×C4 | #14523248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523248 | 2 |
| C2×#16861168 | 2 |
| #22549782 | 2 |
| #22549778 | 2 |
| #22549755 | 2 |
| C4×(C2×D127)⋊C4 | 2 |
| C22×C42×C127 | 2 |
| #2297 | 127 |