Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
198 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 47 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. C22×D28 | C2 | semidirect |
| 2. #6493 | C2 | semidirect |
| 3. C2×D56 | C2 | semidirect |
| 4. C7×C22⋊C8 | C2 | semidirect |
| 5. #6395 | C2 | semidirect |
| 12. C2×D28 | C22 | semidirect |
| 13. C2×C7×C8 | C22 | semidirect |
| 15. C4⋊Dic7 | C22 | semidirect |
| 32. D28 | D4 | semidirect |
| 38. C22⋊C8 | D7 | semidirect |
| 41. C22×C7 | D8 | semidirect |
| 61. C2×C8 | C2×D7 | semidirect |
| 86. C7 | #447 | semidirect |
| 96. C22 | D56 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D28 | 2 |
| #6493 | 2 |
| C2×D56 | 2 |
| C7×C22⋊C8 | 2 |
| #6395 | 2 |
| #447 | 7 |