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 |
|---|---|---|
| 1. C7×#117 | C2 | semidirect |
| 3. C22⋊(C7⋊C8) | C2 | semidirect |
| 4. #6383 | C2 | semidirect |
| 5. #6383 | C2 | semidirect |
| 6. #6382 | C2 | semidirect |
| 7. #6381 | C2 | semidirect |
| 35. #117 | 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 |
|---|---|
| C7×#117 | 2 |
| #6493 | 2 |
| C22⋊(C7⋊C8) | 2 |
| #6383 | 2 |
| #6382 | 2 |
| #6381 | 2 |
| #482 | 7 |