Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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×C8×D7 | C2 | semidirect |
| 3. #6455 | C2 | semidirect |
| 4. C7×#103 | C2 | semidirect |
| 5. #6409 | C2 | semidirect |
| 6. #6395 | C2 | semidirect |
| 7. #6383 | C2 | semidirect |
| 10. #1161 | C4 | semidirect |
| 44. #103 | D7 | semidirect |
| 96. C7 | #416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1161 | 2 |
| C2×C8×D7 | 2 |
| #6455 | 2 |
| C7×#103 | 2 |
| #6409 | 2 |
| #6395 | 2 |
| #6383 | 2 |
| #416 | 7 |