Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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×#16861152 | C2 | semidirect |
| 3. #22549676 | C2 | semidirect |
| 4. C22⋊(C127⋊C16) | C2 | semidirect |
| 5. #467×C127 | C2 | semidirect |
| 11. C2×C127⋊C16 | C22 | semidirect |
| 12. C2×Q16×C127 | C22 | semidirect |
| 15. #107×C127 | C22 | semidirect |
| 55. C22×C127 | SD32 | semidirect |
| 72. C127 | #2187 | semidirect |
| 75. #467 | D127 | semidirect |
| 79. C2×Q16 | C2×D127 | semidirect |
| 87. #107 | C2×D127 | semidirect |
| 131. C22 | #16861152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1016 | 2 |
| C2×#16861152 | 2 |
| #22549676 | 2 |
| C22⋊(C127⋊C16) | 2 |
| #467×C127 | 2 |
| #2187 | 127 |