Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
| 2. #22551590 | C2 | semidirect |
| 3. #22551571 | C2 | semidirect |
| 4. #22551568 | C2 | semidirect |
| 5. Q8×Dic257 | C2 | semidirect |
| 7. C22×Q8×C257 | C2 | semidirect |
| 24. C22⋊D257 | Q8 | direct (N × H) |
| 31. Q8×C257 | D4 | semidirect |
| 37. C22×C257 | C2×Q8 | semidirect |
| 41. C2×D257 | C2×Q8 | semidirect |
| 46. Dic257 | C2×Q8 | semidirect |
| 52. C257 | D4×Q8 | semidirect |
| 55. C22×Q8 | D257 | semidirect |
| 79. Q8 | C22⋊D257 | direct (N × H) |
| 93. 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 |
| #22551590 | 2 |
| #22551571 | 2 |
| #22551568 | 2 |
| Q8×Dic257 | 2 |
| C4×C22⋊D257 | 2 |
| C22×Q8×C257 | 2 |
| D4×Q8 | 257 |