Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. #6450 | C2 | semidirect |
| 4. C7×#106 | C2 | semidirect |
| 5. C8×Dic7 | C2 | semidirect |
| 6. #6384 | C2 | semidirect |
| 19. #1132 | C4 | semidirect |
| 32. Dic14 | C2×C4 | semidirect |
| 33. C7×C8 | C2×C4 | semidirect |
| 38. #106 | D7 | semidirect |
| 52. Dic7 | SD16 | semidirect |
| 82. C8 | C4×D7 | semidirect |
| 83. C7 | C4×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1132 | 2 |
| #6456 | 2 |
| #6450 | 2 |
| C7×#106 | 2 |
| C8×Dic7 | 2 |
| #6384 | 2 |
| #6383 | 2 |
| C4×SD16 | 7 |