Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #22551617 | C2 | semidirect |
| 2. C2×#16861603 | C2 | semidirect |
| 3. #22551599 | C2 | semidirect |
| 4. #22551527 | C2 | semidirect |
| 5. #22551509 | C2 | semidirect |
| 6. #22551508 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C257 | C2 | semidirect |
| 53. C257 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551617 | 2 |
| C2×#16861603 | 2 |
| #22551599 | 2 |
| #22551527 | 2 |
| #22551509 | 2 |
| #22551508 | 2 |
| AGL(1,ℤ/8)×C257 | 2 |
| #472 | 257 |