Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. C2×C4⋊Dic7 | C2 | semidirect |
| 5. C2×Dic7⋊C4 | C2 | semidirect |
| 6. C2×Dic7⋊C4 | C2 | semidirect |
| 7. C2×C4×Dic7 | C2 | semidirect |
| 8. #6442 | C2 | direct (N × H) |
| 19. C4⋊Dic7 | C22 | semidirect |
| 20. Dic7⋊C4 | C22 | semidirect |
| 21. Dic7⋊C4 | C22 | semidirect |
| 22. C4×Dic7 | C22 | semidirect |
| 78. C2×C7 | #126 | semidirect |
| 99. C7 | C2×#126 | semidirect |
| 115. C2 | #6442 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C22⋊C4 | 2 |
| C2×C22⋊Dic7 | 2 |
| C2×C4⋊Dic7 | 2 |
| C2×Dic7⋊C4 | 2 |
| C2×C4×Dic7 | 2 |
| #6442 | 2 |
| C2×#126 | 7 |