Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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. C7×#137 | C2 | semidirect |
| 3. #6507 | C2 | semidirect |
| 4. #6505 | C2 | semidirect |
| 5. #6411 | C2 | semidirect |
| 6. #6399 | C2 | semidirect |
| 7. #6398 | C2 | semidirect |
| 50. #137 | D7 | semidirect |
| 108. C7 | #456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6554 | 2 |
| C7×#137 | 2 |
| #6507 | 2 |
| #6505 | 2 |
| #6411 | 2 |
| #6399 | 2 |
| #6398 | 2 |
| #456 | 7 |