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 |
|---|---|---|
| 1. C7×#137 | C2 | semidirect |
| 3. #6511 | C2 | semidirect |
| 4. C2×#1143 | C2 | semidirect |
| 5. #6410 | C2 | semidirect |
| 6. #6397 | C2 | semidirect |
| 7. #6396 | C2 | semidirect |
| 40. #137 | D7 | 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×#137 | 2 |
| #6512 | 2 |
| #6511 | 2 |
| C2×#1143 | 2 |
| #6410 | 2 |
| #6397 | 2 |
| #6396 | 2 |
| #471 | 7 |