Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 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. C7×#131 | C2 | semidirect |
| 3. #6464 | C2 | semidirect |
| 4. #6411 | C2 | semidirect |
| 5. #6399 | C2 | semidirect |
| 6. #6396 | C2 | semidirect |
| 7. #6389 | C2 | semidirect |
| 14. #1144 | C4 | semidirect |
| 15. #1143 | C4 | semidirect |
| 16. #1142 | C4 | semidirect |
| 17. #1141 | C4 | semidirect |
| 42. #131 | D7 | semidirect |
| 90. C7 | #444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#131 | 2 |
| #6513 | 2 |
| #6464 | 2 |
| #6411 | 2 |
| #6399 | 2 |
| #6396 | 2 |
| #6389 | 2 |
| #444 | 7 |