Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
324 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 13. C4⋊Q8×C127 | C4 | semidirect |
| 61. C4×C127 | #103 | semidirect |
| 72. C127 | #1981 | semidirect |
| 80. C4⋊Q8 | Dic127 | semidirect |
| 134. C4 | #16861133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C127⋊C8) | 2 |
| C2×#16861133 | 2 |
| C4×C4⋊Dic127 | 2 |
| C2×C4⋊Q8×C127 | 2 |
| #1981 | 127 |