Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
308 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 14. C4×Q8×C127 | C4 | semidirect |
| 52. Q8×C127 | C4⋊C4 | semidirect |
| 81. C4×C127 | #103 | semidirect |
| 95. C127 | #1803 | semidirect |
| 104. C4×Q8 | Dic127 | semidirect |
| 143. Q8 | C4⋊Dic127 | semidirect |
| 177. 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 |
| #22549746 | 2 |
| #22549638 | 2 |
| C2×C4×Q8×C127 | 2 |
| #1803 | 127 |