Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
210 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 71 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×C22⋊Dic257 | C2 | semidirect |
| 2. #22551507 | C2 | direct (N × H) |
| 6. C22⋊Dic257 | C22 | semidirect |
| 7. C24×C257 | C4 | semidirect |
| 11. C2×D4×C257 | C4 | semidirect |
| 13. C22×C4×C257 | C4 | semidirect |
| 22. C23×C257 | C2×C4 | semidirect |
| 30. C2×C4×C257 | C2×C4 | semidirect |
| 52. C2×C257 | #99 | semidirect |
| 54. C257 | C2×#99 | semidirect |
| 59. C24 | Dic257 | semidirect |
| 63. C2×D4 | Dic257 | semidirect |
| 66. C22×C4 | Dic257 | semidirect |
| 75. C23 | C2×Dic257 | semidirect |
| 85. C2×C4 | C2×Dic257 | semidirect |
| 107. C2 | #22551507 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Dic257 | 2 |
| #22551507 | 2 |
| C22×D4×C257 | 2 |
| C2×#99 | 257 |