Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 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. C7×#117 | C2 | semidirect |
| 3. C2×C4×Dic7 | C2 | semidirect |
| 4. #6456 | C2 | semidirect |
| 5. #6450 | C2 | semidirect |
| 6. (C22⋊D7)⋊C4 | C2 | semidirect |
| 7. #6435 | C2 | semidirect |
| 8. C42×D7 | C2 | semidirect |
| 12. #1157 | C4 | semidirect |
| 29. C2×C4×C7 | C2×C4 | semidirect |
| 33. C22⋊D7 | C2×C4 | semidirect |
| 38. D28 | C2×C4 | semidirect |
| 40. C4×D7 | C2×C4 | semidirect |
| 41. Dic14 | C2×C4 | semidirect |
| 47. #117 | D7 | semidirect |
| 60. Dic7 | #41 | semidirect |
| 93. C2×C4 | C4×D7 | semidirect |
| 97. C7 | C4×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157 | 2 |
| C7×#117 | 2 |
| C2×C4×Dic7 | 2 |
| #6456 | 2 |
| #6450 | 2 |
| (C22⋊D7)⋊C4 | 2 |
| #6435 | 2 |
| C42×D7 | 2 |
| C4×#41 | 7 |