Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 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 |
|---|---|---|
| 2. #6514 | C2 | semidirect |
| 3. #6511 | C2 | semidirect |
| 4. C2×#1142 | C2 | semidirect |
| 5. #6407 | C2 | semidirect |
| 6. #6398 | C2 | semidirect |
| 7. #6396 | C2 | semidirect |
| 90. C7 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×AGL(1,ℤ/8) | 2 |
| #6514 | 2 |
| #6511 | 2 |
| C2×#1142 | 2 |
| #6407 | 2 |
| #6398 | 2 |
| #6396 | 2 |
| #471 | 7 |