Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
120 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 57 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. Q8×Dic7 | C2 | semidirect |
| 4. #6409 | C2 | semidirect |
| 6. #6392 | C2 | semidirect |
| 7. #6389 | C2 | semidirect |
| 11. C7×SD16 | C4 | semidirect |
| 23. C7×Q8 | C2×C4 | semidirect |
| 33. C7×C8 | C2×C4 | semidirect |
| 56. SD16 | Dic7 | semidirect |
| 71. Q8 | C2×Dic7 | semidirect |
| 82. C8 | C2×Dic7 | semidirect |
| 83. C7 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×SD16 | 2 |
| Q8×Dic7 | 2 |
| D4×Dic7 | 2 |
| #6409 | 2 |
| #6406 | 2 |
| #6392 | 2 |
| #6389 | 2 |
| #440 | 7 |