Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C7×C22⋊Q8 | C2 | semidirect |
| 3. C2×#1144 | C2 | semidirect |
| 4. C2×#1143 | C2 | semidirect |
| 5. C22⋊(C7⋊C8) | C2 | semidirect |
| 6. #6384 | C2 | semidirect |
| 7. #6383 | C2 | semidirect |
| 46. C22⋊Q8 | D7 | semidirect |
| 102. C7 | #452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157 | 2 |
| C7×C22⋊Q8 | 2 |
| C2×#1144 | 2 |
| C2×#1143 | 2 |
| C22⋊(C7⋊C8) | 2 |
| #6384 | 2 |
| #6383 | 2 |
| #452 | 7 |