Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 2. C7×C22⋊Q8 | C2 | semidirect |
| 3. C2×#1143 | C2 | semidirect |
| 4. C22⋊(C7⋊C8) | C2 | semidirect |
| 5. #6383 | C2 | semidirect |
| 7. C2×C7×Q8 | C22 | semidirect |
| 13. C7×C4⋊C4 | C22 | semidirect |
| 16. C2×C7⋊C8 | C22 | semidirect |
| 35. C22⋊Q8 | D7 | semidirect |
| 40. C22×C7 | SD16 | semidirect |
| 51. C2×Q8 | C2×D7 | semidirect |
| 59. C4⋊C4 | C2×D7 | semidirect |
| 81. C7 | #450 | semidirect |
| 88. C22 | #1143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D28 | 2 |
| C7×C22⋊Q8 | 2 |
| C2×#1143 | 2 |
| C22⋊(C7⋊C8) | 2 |
| #6383 | 2 |
| #450 | 7 |