Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 565 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×#16861204 | C2 | direct (N × H) |
| 2. C22×C4⋊Dic127 | C2 | semidirect |
| 3. C22×Dic127⋊C4 | C2 | semidirect |
| 7. C22×C4×Dic127 | C2 | semidirect |
| 8. C22×C4⋊C4×C127 | C2 | semidirect |
| 13. #16861204 | C22 | direct (N × H) |
| 14. C2×C4⋊Dic127 | C22 | semidirect |
| 15. C2×Dic127⋊C4 | C22 | semidirect |
| 19. C2×C4×Dic127 | C22 | semidirect |
| 23. C2×C4⋊C4×C127 | C22 | semidirect |
| 34. C4⋊Dic127 | C23 | semidirect |
| 35. Dic127⋊C4 | C23 | semidirect |
| 39. C4×Dic127 | C23 | semidirect |
| 47. C4⋊C4×C127 | C23 | semidirect |
| 69. C22×C127 | #126 | semidirect |
| 84. C2×C127 | C2×#126 | semidirect |
| 90. C127 | C22×#126 | semidirect |
| 94. C22×C4⋊C4 | D127 | semidirect |
| 109. C2×C4⋊C4 | C2×D127 | semidirect |
| 133. C4⋊C4 | C22×D127 | semidirect |
| 163. C22 | #16861204 | direct (N × H) |
| 175. C2 | C2×#16861204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861204 | 2 |
| C22×C4⋊Dic127 | 2 |
| C22×Dic127⋊C4 | 2 |
| C22×(C2×D127)⋊C4 | 2 |
| C22×C4×Dic127 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C22×#126 | 127 |