Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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. #22549727 | C2 | semidirect |
| 3. C4×C22⋊Dic127 | C2 | semidirect |
| 4. #22549723 | C2 | semidirect |
| 5. #22549721 | C2 | semidirect |
| 6. #95×D127 | C2 | semidirect |
| 7. C2×#95×C127 | C2 | semidirect |
| 10. C4×C22⋊D127 | C4 | semidirect |
| 27. C2×C4×D127 | C2×C4 | semidirect |
| 28. Dic127⋊C4 | C2×C4 | semidirect |
| 29. C22⋊Dic127 | C2×C4 | semidirect |
| 30. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 32. C4×Dic127 | C2×C4 | semidirect |
| 35. C22×C4×C127 | C2×C4 | semidirect |
| 41. C22⋊D127 | C42 | semidirect |
| 78. C127 | #2275 | semidirect |
| 85. C2×#95 | D127 | semidirect |
| 108. C22×C4 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D127 | 2 |
| #22549727 | 2 |
| C4×C22⋊Dic127 | 2 |
| #22549723 | 2 |
| #22549721 | 2 |
| #95×D127 | 2 |
| C2×#95×C127 | 2 |
| #2275 | 127 |