Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
840 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 469 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. #22549722 | C2 | direct (N × H) |
| 6. C2×C4×Dic127 | C4 | semidirect |
| 11. C2×C42×C127 | C4 | semidirect |
| 16. C4×Dic127 | C2×C4 | semidirect |
| 24. C42×C127 | C2×C4 | semidirect |
| 47. C2×C127 | #376 | semidirect |
| 52. C127 | C2×#376 | semidirect |
| 62. C2×C42 | Dic127 | semidirect |
| 76. C42 | C2×Dic127 | semidirect |
| 99. C2 | #22549722 | 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 |
| #22549722 | 2 |
| C2×C127⋊#95 | 2 |
| C22×C42×C127 | 2 |
| C2×#376 | 127 |