Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
174 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 51 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×#16861152 | C2 | semidirect |
| 3. Q16×Dic127 | C2 | semidirect |
| 4. Dic127⋊C16 | C2 | semidirect |
| 5. #22549678 | C2 | semidirect |
| 6. #22549677 | C2 | semidirect |
| 7. C2×SD32×C127 | C2 | semidirect |
| 36. Q16×C127 | D4 | semidirect |
| 71. Dic127 | SD32 | semidirect |
| 78. C127 | #2207 | semidirect |
| 80. C2×SD32 | D127 | semidirect |
| 105. Q16 | C22⋊D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861152 | 2 |
| #22550251 | 2 |
| Q16×Dic127 | 2 |
| Dic127⋊C16 | 2 |
| #22549678 | 2 |
| #22549677 | 2 |
| C2×SD32×C127 | 2 |
| #2207 | 127 |