Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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×#16861607 | C2 | semidirect |
| 2. C2×#16861606 | C2 | semidirect |
| 3. C2×#16861605 | C2 | semidirect |
| 4. #22551590 | C2 | semidirect |
| 6. C8×Dic257 | C2 | semidirect |
| 7. C2×SD16×C257 | C2 | semidirect |
| 29. #14523339 | D4 | semidirect |
| 37. C8×C257 | D4 | semidirect |
| 47. Dic257 | SD16 | semidirect |
| 52. C257 | #492 | semidirect |
| 57. C2×SD16 | D257 | semidirect |
| 90. C8 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861607 | 2 |
| C2×#16861606 | 2 |
| C2×#16861605 | 2 |
| #22551590 | 2 |
| #22551588 | 2 |
| C8×Dic257 | 2 |
| C2×SD16×C257 | 2 |
| #492 | 257 |