Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 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. C23×C127⋊C8 | C2 | semidirect |
| 2. C22×C4⋊Dic127 | C2 | semidirect |
| 3. C2×#16861130 | C2 | direct (N × H) |
| 7. C22×C127⋊C8 | C22 | semidirect |
| 9. C2×C4⋊Dic127 | C22 | semidirect |
| 10. #16861130 | C22 | direct (N × H) |
| 14. C22×D4×C127 | C4 | semidirect |
| 20. C2×C127⋊C8 | C23 | semidirect |
| 22. C4⋊Dic127 | C23 | semidirect |
| 31. C2×D4×C127 | C2×C4 | semidirect |
| 51. D4×C127 | C22×C4 | semidirect |
| 61. C22×C127 | #102 | semidirect |
| 71. C2×C127 | C2×#102 | semidirect |
| 76. C127 | C22×#102 | semidirect |
| 84. C22×D4 | Dic127 | semidirect |
| 101. C2×D4 | C2×Dic127 | semidirect |
| 124. D4 | C22×Dic127 | semidirect |
| 137. C22 | #16861130 | direct (N × H) |
| 147. C2 | C2×#16861130 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C127⋊C8 | 2 |
| C22×C4⋊Dic127 | 2 |
| C2×#16861130 | 2 |
| C23×D4×C127 | 2 |
| C22×#102 | 127 |