Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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. D7×C4⋊C4 | C2 | semidirect |
| 3. C7×#102 | C2 | semidirect |
| 4. #6406 | C2 | semidirect |
| 5. (C2×D7)⋊C8 | C2 | semidirect |
| 6. #6391 | C2 | semidirect |
| 7. #6382 | C2 | semidirect |
| 40. #102 | D7 | semidirect |
| 86. C7 | #481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6501 | 2 |
| D7×C4⋊C4 | 2 |
| C7×#102 | 2 |
| #6406 | 2 |
| (C2×D7)⋊C8 | 2 |
| #6391 | 2 |
| #6382 | 2 |
| #481 | 7 |