Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1192 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 645 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×#16861200 | C2 | direct (N × H) |
| 10. #16861200 | C22 | direct (N × H) |
| 48. C22×C127 | #125 | semidirect |
| 58. C2×C127 | C2×#125 | semidirect |
| 63. C127 | C22×#125 | semidirect |
| 111. C22 | #16861200 | direct (N × H) |
| 121. C2 | C2×#16861200 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861200 | 2 |
| C22×C4⋊Dic127 | 2 |
| C22×Dic127⋊C4 | 2 |
| C22×C4×Dic127 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C22×#125 | 127 |