Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
152 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C2×#1144 | C2 | semidirect |
| 3. C2×#1142 | C2 | semidirect |
| 4. #6487 | C2 | semidirect |
| 5. #6409 | C2 | semidirect |
| 6. #6406 | C2 | semidirect |
| 7. C22⋊(C7⋊C8) | C2 | semidirect |
| 102. C7 | #452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41 | 2 |
| C2×#1144 | 2 |
| C2×#1142 | 2 |
| #6487 | 2 |
| #6409 | 2 |
| #6406 | 2 |
| C22⋊(C7⋊C8) | 2 |
| #452 | 7 |