Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22551587 | C2 | direct (N × H) |
| 2. C2×C4⋊Dic257 | C2 | semidirect |
| 3. C2×#16861597 | C2 | semidirect |
| 7. C2×C4×Dic257 | C2 | semidirect |
| 8. C2×C4⋊C4×C257 | C2 | semidirect |
| 13. C4⋊Dic257 | C22 | semidirect |
| 14. #16861597 | C22 | semidirect |
| 18. C4×Dic257 | C22 | semidirect |
| 22. C4⋊C4×C257 | C22 | semidirect |
| 54. C2×C257 | #126 | semidirect |
| 59. C257 | C2×#126 | semidirect |
| 64. C2×C4⋊C4 | D257 | semidirect |
| 78. C4⋊C4 | C2×D257 | semidirect |
| 115. C2 | #22551587 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551587 | 2 |
| C2×C4⋊Dic257 | 2 |
| C2×#16861597 | 2 |
| C2×#16861595 | 2 |
| C2×C4×Dic257 | 2 |
| C2×C4⋊C4×C257 | 2 |
| C2×#126 | 257 |