Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
232 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 12. #16861144 | C4 | semidirect |
| 13. #16861142 | C4 | semidirect |
| 14. #16861140 | C4 | semidirect |
| 18. C4×C127⋊C8 | C4 | semidirect |
| 80. C127 | #1772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861144 | 2 |
| #22549912 | 2 |
| #22549834 | 2 |
| #22549832 | 2 |
| C2×C4×C127⋊C8 | 2 |
| #22549636 | 2 |
| #339×C127 | 2 |
| #1772 | 127 |