Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 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 |
| 2. C2×#16861149 | C2 | semidirect |
| 4. #22549701 | C2 | semidirect |
| 5. #22549680 | C2 | semidirect |
| 6. #22549676 | C2 | semidirect |
| 7. #467×C127 | C2 | semidirect |
| 28. C127⋊C16 | D4 | semidirect |
| 76. C127 | #2220 | semidirect |
| 79. #467 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861152 | 2 |
| C2×#16861149 | 2 |
| #22550112 | 2 |
| #22549701 | 2 |
| #22549680 | 2 |
| #22549676 | 2 |
| #467×C127 | 2 |
| #2220 | 127 |