Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 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. #6489 | C2 | semidirect |
| 3. C7×C22⋊C8 | C2 | semidirect |
| 4. #6395 | C2 | semidirect |
| 5. #6395 | C2 | semidirect |
| 6. #6392 | C2 | semidirect |
| 7. #6391 | C2 | semidirect |
| 40. C22⋊C8 | D7 | semidirect |
| 84. C7 | #482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6493 | 2 |
| #6489 | 2 |
| C7×C22⋊C8 | 2 |
| #6395 | 2 |
| #6392 | 2 |
| #6391 | 2 |
| #482 | 7 |