Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
224 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 8. #16861145 | C4 | semidirect |
| 9. #16861143 | C4 | semidirect |
| 10. #16861141 | C4 | semidirect |
| 16. #97×C127 | C4 | semidirect |
| 63. C127 | #1773 | semidirect |
| 78. #97 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861145 | 2 |
| #22549914 | 2 |
| #22549831 | 2 |
| #22549636 | 2 |
| C2×#97×C127 | 2 |
| #1773 | 127 |