Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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×#1142 | C2 | semidirect |
| 3. #6487 | C2 | semidirect |
| 4. C22×C7⋊C8 | C2 | semidirect |
| 5. #6406 | C2 | semidirect |
| 6. #6384 | C2 | semidirect |
| 7. #6382 | C2 | semidirect |
| 37. C7⋊C8 | D4 | semidirect |
| 50. C22×C7 | SD16 | semidirect |
| 92. C7 | #465 | semidirect |
| 98. C22 | #1142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#121 | 2 |
| C2×#1142 | 2 |
| #6487 | 2 |
| C22×C7⋊C8 | 2 |
| #6406 | 2 |
| #6384 | 2 |
| #6382 | 2 |
| #465 | 7 |