Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22549904 | C2 | semidirect |
| 4. C2×C4×C127⋊C8 | C2 | semidirect |
| 5. #22549640 | C2 | semidirect |
| 6. #22549636 | C2 | semidirect |
| 13. #16861133 | C4 | semidirect |
| 14. #16861130 | C4 | semidirect |
| 91. C127 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549904 | 2 |
| #22549872 | 2 |
| #22549843 | 2 |
| C2×C4×C127⋊C8 | 2 |
| #22549640 | 2 |
| #22549636 | 2 |
| C2×#104×C127 | 2 |
| #1937 | 127 |