Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1232 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 349 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. C22×Dic127⋊C4 | C2 | semidirect |
| 4. #22549735 | C2 | direct (N × H) |
| 5. C2×C127⋊#95 | C2 | semidirect |
| 6. C2×#95×C127 | C2 | semidirect |
| 11. C22×C4×D127 | C4 | semidirect |
| 14. C2×Dic127⋊C4 | C22 | semidirect |
| 17. C127⋊#95 | C22 | semidirect |
| 20. #95×C127 | C22 | semidirect |
| 36. C2×C4×D127 | C2×C4 | semidirect |
| 53. C22×D127 | C4⋊C4 | semidirect |
| 61. C2×Dic127 | C22⋊C4 | semidirect |
| 93. C2×D127 | C2×C4⋊C4 | semidirect |
| 97. Dic127 | C2×C22⋊C4 | semidirect |
| 98. C2×C127 | #380 | semidirect |
| 106. C127 | C2×#380 | semidirect |
| 112. C2×#95 | D127 | semidirect |
| 126. #95 | C2×D127 | semidirect |
| 205. C2 | #22549735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D127 | 2 |
| C22×Dic127⋊C4 | 2 |
| C22×(C2×D127)⋊C4 | 2 |
| #22549735 | 2 |
| C2×C127⋊#95 | 2 |
| C2×#95×C127 | 2 |
| C2×#380 | 127 |