Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1360 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 405 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. C22×C4⋊Dic127 | C2 | semidirect |
| 2. C22×C22⋊Dic127 | C2 | semidirect |
| 3. C22×C4×Dic127 | C2 | semidirect |
| 4. #22549779 | C2 | direct (N × H) |
| 9. C2×C4⋊Dic127 | C22 | semidirect |
| 11. C2×C22⋊Dic127 | C22 | semidirect |
| 13. C2×C4×Dic127 | C22 | semidirect |
| 17. C22×D4×C127 | C4 | semidirect |
| 24. C22×Dic127 | D4 | semidirect |
| 40. C2×D4×C127 | C2×C4 | semidirect |
| 51. C2×Dic127 | C2×D4 | semidirect |
| 69. C2×C4×C127 | C22⋊C4 | semidirect |
| 89. C4×C127 | C2×C22⋊C4 | semidirect |
| 93. C2×C127 | #390 | semidirect |
| 100. C127 | C2×#390 | semidirect |
| 109. C22×D4 | Dic127 | semidirect |
| 130. C2×D4 | C2×Dic127 | semidirect |
| 169. C2×C4 | C22⋊Dic127 | semidirect |
| 191. C4 | C2×C22⋊Dic127 | semidirect |
| 193. C2 | #22549779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic127 | 2 |
| C22×C22⋊Dic127 | 2 |
| C22×C4×Dic127 | 2 |
| #22549779 | 2 |
| C23×D4×C127 | 2 |
| C2×#390 | 127 |