Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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×C7×C22⋊C4 | C2 | semidirect |
| 3. C2×C22⋊Dic7 | C2 | semidirect |
| 4. #6380 | C2 | direct (N × H) |
| 6. C23×D7 | C4 | semidirect |
| 12. C2×C22⋊D7 | C4 | semidirect |
| 15. C22×Dic7 | C4 | semidirect |
| 17. C7×C22⋊C4 | C22 | semidirect |
| 19. C22⋊Dic7 | C22 | semidirect |
| 32. C22×D7 | C2×C4 | semidirect |
| 43. C2×Dic7 | C2×C4 | semidirect |
| 46. C2×C22⋊C4 | D7 | semidirect |
| 83. C22⋊C4 | C2×D7 | semidirect |
| 90. C2×C7 | #99 | semidirect |
| 116. C7 | C2×#99 | semidirect |
| 145. C2 | #6380 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D7 | 2 |
| C2×C7×C22⋊C4 | 2 |
| C2×C22⋊Dic7 | 2 |
| #6380 | 2 |
| C2×#99 | 7 |