Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
130 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 43 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. #6510 | C2 | semidirect |
| 3. C2×#1144 | C2 | semidirect |
| 4. #6499 | C2 | semidirect |
| 6. C2×#1132 | C2 | semidirect |
| 7. C8×Dic7 | C2 | semidirect |
| 40. C2×SD16 | D7 | semidirect |
| 88. C7 | #495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×SD16 | 2 |
| #6510 | 2 |
| C2×#1144 | 2 |
| #6499 | 2 |
| C2×#1141 | 2 |
| C2×#1132 | 2 |
| C8×Dic7 | 2 |
| #495 | 7 |