Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. #6507 | C2 | semidirect |
| 5. C7×#103 | C2 | semidirect |
| 6. Dic7⋊C8 | C2 | semidirect |
| 7. #6384 | C2 | semidirect |
| 44. #103 | D7 | semidirect |
| 55. Dic7 | SD16 | semidirect |
| 89. C7 | #461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6507 | 2 |
| C2×#1143 | 2 |
| C2×#1132 | 2 |
| #6456 | 2 |
| C7×#103 | 2 |
| Dic7⋊C8 | 2 |
| #6384 | 2 |
| #461 | 7 |