Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 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. C22×Dic514 | C2 | semidirect |
| 3. #22551499 | C2 | semidirect |
| 4. #22551499 | C2 | semidirect |
| 26. C23×C257 | Q8 | semidirect |
| 52. C257 | #393 | semidirect |
| 72. C23 | Dic514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic514 | 2 |
| C2×C22⋊Dic257 | 2 |
| #22551499 | 2 |
| C2×C22⋊C4×C257 | 2 |
| #393 | 257 |