Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×C4×D7 | C2 | semidirect |
| 3. C2×C7×C4⋊C4 | C2 | semidirect |
| 4. C2×(C2×D7)⋊C4 | C2 | semidirect |
| 5. C2×(C2×D7)⋊C4 | C2 | semidirect |
| 6. C2×(C2×D7)⋊C4 | C2 | semidirect |
| 7. C2×Dic7⋊C4 | C2 | semidirect |
| 8. #6457 | C2 | direct (N × H) |
| 19. C2×C4×D7 | C22 | semidirect |
| 20. C7×C4⋊C4 | C22 | semidirect |
| 21. (C2×D7)⋊C4 | C22 | semidirect |
| 22. (C2×D7)⋊C4 | C22 | semidirect |
| 23. (C2×D7)⋊C4 | C22 | semidirect |
| 24. Dic7⋊C4 | C22 | semidirect |
| 51. C2×C4⋊C4 | D7 | semidirect |
| 84. C4⋊C4 | C2×D7 | semidirect |
| 88. C2×C7 | #123 | semidirect |
| 115. C7 | C2×#123 | semidirect |
| 135. C2 | #6457 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D28 | 2 |
| C22×C4×D7 | 2 |
| C2×C7×C4⋊C4 | 2 |
| C2×(C2×D7)⋊C4 | 2 |
| C2×Dic7⋊C4 | 2 |
| #6457 | 2 |
| C2×#123 | 7 |