Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. C22×C4×D257 | C2 | semidirect |
| 3. #22551574 | C2 | direct (N × H) |
| 4. C2×C4⋊Dic257 | C2 | semidirect |
| 5. C2×#16861597 | C2 | semidirect |
| 6. C2×C22⋊Dic257 | C2 | semidirect |
| 7. C2×#16861595 | C2 | semidirect |
| 8. C2×C22⋊C4×C257 | C2 | semidirect |
| 16. C2×C4×D257 | C22 | semidirect |
| 17. C4⋊Dic257 | C22 | semidirect |
| 18. #16861597 | C22 | semidirect |
| 19. C22⋊Dic257 | C22 | semidirect |
| 20. #16861595 | C22 | semidirect |
| 24. C22⋊C4×C257 | C22 | semidirect |
| 64. C2×C257 | #123 | semidirect |
| 69. C257 | C2×#123 | semidirect |
| 78. C2×C22⋊C4 | D257 | semidirect |
| 94. C22⋊C4 | C2×D257 | semidirect |
| 135. C2 | #22551574 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D257 | 2 |
| C22×C4×D257 | 2 |
| #22551574 | 2 |
| C2×C4⋊Dic257 | 2 |
| C2×#16861597 | 2 |
| C2×C22⋊Dic257 | 2 |
| C2×#16861595 | 2 |
| C2×C22⋊C4×C257 | 2 |
| C2×#123 | 257 |