Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
134 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. C4×C7×D4 | C2 | semidirect |
| 3. C4×D28 | C2 | semidirect |
| 4. #6406 | C2 | semidirect |
| 5. #6383 | C2 | semidirect |
| 6. #6381 | C2 | semidirect |
| 7. C4×C7⋊C8 | C2 | semidirect |
| 15. #1141 | C4 | direct (N × H) |
| 24. C7×D4 | C2×C4 | semidirect |
| 32. D28 | C2×C4 | semidirect |
| 35. C7⋊C8 | C2×C4 | semidirect |
| 38. C4×D4 | D7 | semidirect |
| 52. C4×C7 | D8 | semidirect |
| 78. D4 | C4×D7 | semidirect |
| 88. C7 | C4×D8 | semidirect |
| 99. C4 | #1141 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×D4 | 2 |
| C2×#1141 | 2 |
| C4×D28 | 2 |
| #6406 | 2 |
| #6383 | 2 |
| #6381 | 2 |
| C4×C7⋊C8 | 2 |
| C4×D8 | 7 |