Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 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 |
|---|---|---|
| 1. C2×#16861154 | C2 | semidirect |
| 2. C2×#16861153 | C2 | semidirect |
| 3. C2×#16861150 | C2 | semidirect |
| 4. #22550259 | C2 | semidirect |
| 5. #22550251 | C2 | semidirect |
| 6. #22549651 | C2 | semidirect |
| 7. C2×D16×C127 | C2 | semidirect |
| 35. C127⋊C16 | D4 | semidirect |
| 43. C16×C127 | D4 | semidirect |
| 79. C127 | #2250 | semidirect |
| 83. C2×D16 | D127 | semidirect |
| 122. C16 | C22⋊D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861154 | 2 |
| C2×#16861153 | 2 |
| C2×#16861150 | 2 |
| #22550259 | 2 |
| #22550251 | 2 |
| #22549651 | 2 |
| C2×D16×C127 | 2 |
| #2250 | 127 |