Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×Dic14 | C2 | semidirect |
| 3. C2×C7×C4⋊C4 | C2 | semidirect |
| 6. C2×Dic7⋊C4 | C2 | semidirect |
| 7. C2×Dic7⋊C4 | C2 | semidirect |
| 8. #6459 | C2 | direct (N × H) |
| 19. C2×Dic14 | C22 | semidirect |
| 20. C7×C4⋊C4 | C22 | semidirect |
| 23. Dic7⋊C4 | C22 | semidirect |
| 24. Dic7⋊C4 | C22 | semidirect |
| 29. C22×D7 | Q8 | semidirect |
| 50. C2×C4⋊C4 | D7 | semidirect |
| 60. C2×D7 | C2×Q8 | semidirect |
| 80. C4⋊C4 | C2×D7 | semidirect |
| 83. C2×C7 | C22⋊Q8 | semidirect |
| 107. C7 | C2×C22⋊Q8 | semidirect |
| 123. C2 | #6459 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D7 | 2 |
| C22×Dic14 | 2 |
| C2×C7×C4⋊C4 | 2 |
| C2×(C2×D7)⋊C4 | 2 |
| C2×Dic7⋊C4 | 2 |
| #6459 | 2 |
| C2×C22⋊Q8 | 7 |