Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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×#16861154 | C2 | semidirect |
| 3. C2×#16861153 | C2 | semidirect |
| 4. #22550118 | C2 | semidirect |
| 5. #22549676 | C2 | semidirect |
| 6. (C2×D127)⋊C16 | C2 | semidirect |
| 7. #357×C127 | C2 | semidirect |
| 9. C2×Dic508 | C22 | semidirect |
| 18. C2×C127⋊C16 | C22 | semidirect |
| 21. C2×C16×C127 | C22 | semidirect |
| 22. #107×C127 | C22 | semidirect |
| 79. C2×D127 | SD32 | semidirect |
| 92. C127 | #2187 | semidirect |
| 98. #357 | D127 | semidirect |
| 112. C2×C16 | C2×D127 | semidirect |
| 113. #107 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D127 | 2 |
| C2×#16861154 | 2 |
| C2×#16861153 | 2 |
| #22550118 | 2 |
| #22549676 | 2 |
| (C2×D127)⋊C16 | 2 |
| #357×C127 | 2 |
| #2187 | 127 |