Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22549780 | C2 | semidirect |
| 3. #22549768 | C2 | semidirect |
| 4. #22549766 | C2 | semidirect |
| 6. #22549750 | C2 | semidirect |
| 7. #22549747 | C2 | semidirect |
| 8. #22549742 | C2 | semidirect |
| 9. #382×C127 | C2 | semidirect |
| 13. #16861197 | C4 | semidirect |
| 35. C2×Dic254 | C2×C4 | semidirect |
| 51. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 52. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 61. C42×C127 | C2×C4 | semidirect |
| 128. C127 | #2379 | semidirect |
| 137. #382 | D127 | semidirect |
| 189. C42 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861197 | 2 |
| #22549780 | 2 |
| #22549768 | 2 |
| #22549766 | 2 |
| #22549754 | 2 |
| #22549750 | 2 |
| #22549747 | 2 |
| #22549742 | 2 |
| #382×C127 | 2 |
| #2379 | 127 |