Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #22549970 | C2 | semidirect |
| 4. #22549701 | C2 | semidirect |
| 5. #22549681 | C2 | semidirect |
| 6. #22549651 | C2 | semidirect |
| 11. #16861153 | C4 | semidirect |
| 23. Dic508 | C2×C4 | semidirect |
| 30. C127⋊C16 | C2×C4 | semidirect |
| 68. C127 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861153 | 2 |
| #22549970 | 2 |
| D8×Dic127 | 2 |
| #22549701 | 2 |
| #22549681 | 2 |
| #22549651 | 2 |
| #357×C127 | 2 |
| #2175 | 127 |