Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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. C22×C7×Q8 | C2 | semidirect |
| 3. #6509 | C2 | direct (N × H) |
| 5. C2×C4⋊Dic7 | C2 | semidirect |
| 6. C2×Dic7⋊C4 | C2 | semidirect |
| 9. C2×C7×Q8 | C22 | semidirect |
| 17. C4⋊Dic7 | C22 | semidirect |
| 18. Dic7⋊C4 | C22 | semidirect |
| 23. C22×D7 | Q8 | semidirect |
| 35. C22×Q8 | D7 | semidirect |
| 48. C2×D7 | C2×Q8 | semidirect |
| 55. C2×Q8 | C2×D7 | semidirect |
| 65. C2×C7 | C22⋊Q8 | semidirect |
| 85. C7 | C2×C22⋊Q8 | semidirect |
| 99. C2 | #6509 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q8 | 2 |
| C22×C4×D7 | 2 |
| #6509 | 2 |
| C2×(C2×D7)⋊C4 | 2 |
| C2×C4⋊Dic7 | 2 |
| C2×Dic7⋊C4 | 2 |
| C2×C22⋊Q8 | 7 |