Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
232 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #22549680 | C2 | direct (N × H) |
| 13. C2×Q16×C127 | C4 | semidirect |
| 28. Q16×C127 | C2×C4 | semidirect |
| 57. C2×C127 | #358 | semidirect |
| 62. C127 | C2×#358 | semidirect |
| 70. C2×Q16 | Dic127 | semidirect |
| 87. Q16 | C2×Dic127 | semidirect |
| 119. C2 | #22549680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C127⋊C16 | 2 |
| C2×#16861143 | 2 |
| #22549680 | 2 |
| C22×Q16×C127 | 2 |
| C2×#358 | 127 |