Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22551572 | C2 | semidirect |
| 2. #22551571 | C2 | semidirect |
| 3. #22551570 | C2 | semidirect |
| 4. #22551570 | C2 | semidirect |
| 5. #22551569 | C2 | semidirect |
| 6. #22551568 | C2 | semidirect |
| 9. C22⋊Q8×C257 | C2 | semidirect |
| 11. C2×Dic514 | C22 | semidirect |
| 12. C2×Dic514 | C22 | semidirect |
| 16. C4⋊Dic257 | C22 | semidirect |
| 17. C4⋊Dic257 | C22 | semidirect |
| 18. #16861597 | C22 | semidirect |
| 19. #16861597 | C22 | semidirect |
| 20. #16861597 | C22 | semidirect |
| 26. C2×Q8×C257 | C22 | semidirect |
| 28. C4⋊C4×C257 | C22 | semidirect |
| 29. C4⋊C4×C257 | C22 | semidirect |
| 33. C22×D257 | Q8 | semidirect |
| 70. C257 | #543 | semidirect |
| 78. C22⋊Q8 | D257 | semidirect |
| 84. C2×Q8 | C2×D257 | semidirect |
| 94. C4⋊C4 | C2×D257 | semidirect |
| 95. C4⋊C4 | C2×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551572 | 2 |
| #22551571 | 2 |
| #22551570 | 2 |
| #22551569 | 2 |
| #22551568 | 2 |
| C2×#16861595 | 2 |
| C22⋊C4×D257 | 2 |
| C22⋊Q8×C257 | 2 |
| #543 | 257 |