Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
110 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 110 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. C2×#1144 | C2 | semidirect |
| 5. C7×#103 | C2 | semidirect |
| 6. #6390 | C2 | semidirect |
| 7. #6382 | C2 | semidirect |
| 43. #103 | D7 | semidirect |
| 87. C7 | #470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6509 | 2 |
| C2×#1144 | 2 |
| C2×#1131 | 2 |
| #6460 | 2 |
| C7×#103 | 2 |
| #6390 | 2 |
| #6382 | 2 |
| #470 | 7 |