Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 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×Q16 | C2 | semidirect |
| 3. #6507 | C2 | semidirect |
| 4. C2×#1144 | C2 | semidirect |
| 7. #6389 | C2 | semidirect |
| 39. C2×Q16 | D7 | semidirect |
| 86. C7 | #497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×Q16 | 2 |
| #6510 | 2 |
| #6507 | 2 |
| C2×#1144 | 2 |
| C2×#1143 | 2 |
| C2×#1132 | 2 |
| #6389 | 2 |
| #497 | 7 |