Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 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. C2×C7×SD16 | C2 | semidirect |
| 2. #6507 | C2 | semidirect |
| 3. C2×#1143 | C2 | semidirect |
| 5. C2×#1142 | C2 | semidirect |
| 6. C2×#1132 | C2 | semidirect |
| 7. C8×Dic7 | C2 | semidirect |
| 37. C7×C8 | D4 | semidirect |
| 38. C7⋊C8 | D4 | semidirect |
| 42. C2×SD16 | D7 | semidirect |
| 55. Dic7 | SD16 | semidirect |
| 89. C8 | C22⋊D7 | semidirect |
| 90. C7 | #492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×SD16 | 2 |
| #6507 | 2 |
| C2×#1143 | 2 |
| #6503 | 2 |
| C2×#1142 | 2 |
| C2×#1132 | 2 |
| C8×Dic7 | 2 |
| #492 | 7 |