Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×Dic14 | C2 | semidirect |
| 3. #6514 | C2 | direct (N × H) |
| 4. C2×#1144 | C2 | semidirect |
| 5. C2×#1142 | C2 | semidirect |
| 6. C2×#1136 | C2 | semidirect |
| 18. C2×Dic14 | C22 | semidirect |
| 19. #1144 | C22 | semidirect |
| 20. #1142 | C22 | semidirect |
| 21. #1136 | C22 | semidirect |
| 77. C2×C7 | #137 | semidirect |
| 98. C7 | C2×#137 | semidirect |
| 111. C2 | #6514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41 | 2 |
| C22×Dic14 | 2 |
| #6514 | 2 |
| C2×#1144 | 2 |
| C2×#1142 | 2 |
| C2×#1136 | 2 |
| C2×#137 | 7 |