Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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. C4×C22⋊D7 | C2 | semidirect |
| 5. (C22⋊D7)⋊C4 | C2 | semidirect |
| 6. D7×C22⋊C4 | C2 | semidirect |
| 7. #6440 | C2 | semidirect |
| 10. C22×C4×C7 | C22 | semidirect |
| 11. C2×C22⋊D7 | C4 | semidirect |
| 15. C22×Dic7 | C22 | semidirect |
| 16. C2×C4×D7 | C22 | semidirect |
| 18. C7×C22⋊C4 | C22 | semidirect |
| 20. C22⋊Dic7 | C22 | semidirect |
| 21. (C2×D7)⋊C4 | C22 | semidirect |
| 22. Dic7⋊C4 | C22 | semidirect |
| 23. C4×Dic7 | C22 | semidirect |
| 26. C23×C7 | C2×C4 | semidirect |
| 31. C22×D7 | C2×C4 | semidirect |
| 35. C22⋊D7 | C2×C4 | semidirect |
| 36. C22⋊D7 | C2×C4 | semidirect |
| 38. C2×Dic7 | C2×C4 | semidirect |
| 48. C2×C22⋊C4 | D7 | semidirect |
| 71. C22×C4 | C2×D7 | semidirect |
| 77. C22⋊C4 | C2×D7 | semidirect |
| 89. C23 | C4×D7 | semidirect |
| 102. C7 | #518 | semidirect |
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 |
| C4×C22⋊D7 | 2 |
| (C22⋊D7)⋊C4 | 2 |
| D7×C22⋊C4 | 2 |
| #6440 | 2 |
| #518 | 7 |