Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×D257 | C2 | semidirect |
| 3. #22551572 | C2 | semidirect |
| 4. #22551571 | C2 | semidirect |
| 5. #22551570 | C2 | semidirect |
| 6. #22551569 | C2 | semidirect |
| 7. #22551568 | C2 | semidirect |
| 8. C4⋊C4×D257 | C2 | semidirect |
| 9. C4⋊C4×D257 | C2 | semidirect |
| 11. C22⋊Q8×C257 | C2 | semidirect |
| 13. C2×Dic514 | C22 | semidirect |
| 14. C2×Dic514 | C22 | semidirect |
| 24. C4⋊Dic257 | C22 | semidirect |
| 25. C4⋊Dic257 | C22 | semidirect |
| 26. #16861597 | C22 | semidirect |
| 27. #16861597 | C22 | semidirect |
| 28. #16861597 | C22 | semidirect |
| 32. C2×Q8×C257 | C22 | semidirect |
| 34. C4⋊C4×C257 | C22 | semidirect |
| 35. C4⋊C4×C257 | C22 | semidirect |
| 39. C22×D257 | Q8 | semidirect |
| 64. C22×C257 | C2×Q8 | semidirect |
| 71. C2×D257 | C2×Q8 | semidirect |
| 86. D257 | C22⋊Q8 | direct (N × H) |
| 87. C257 | C2×C22⋊Q8 | semidirect |
| 96. C22⋊Q8 | D257 | direct (N × H) |
| 104. C2×Q8 | C2×D257 | semidirect |
| 119. C4⋊C4 | C2×D257 | semidirect |
| 120. C4⋊C4 | C2×D257 | semidirect |
| 159. C22 | Q8×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D257 | 2 |
| C22×C4×D257 | 2 |
| #22551572 | 2 |
| #22551571 | 2 |
| #22551570 | 2 |
| #22551569 | 2 |
| #22551568 | 2 |
| C4⋊C4×D257 | 2 |
| C22⋊C4×D257 | 2 |
| C22⋊Q8×C257 | 2 |
| C2×C22⋊Q8 | 257 |