Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×C7×Q16 | C2 | semidirect |
| 4. C2×#1144 | C2 | semidirect |
| 5. #6409 | C2 | semidirect |
| 7. #6390 | C2 | semidirect |
| 45. C2×Q16 | D7 | semidirect |
| 53. C2×D7 | Q16 | semidirect |
| 99. C7 | #451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D7 | 2 |
| C2×C7×Q16 | 2 |
| #6509 | 2 |
| C2×#1144 | 2 |
| #6409 | 2 |
| (C2×D7)⋊C8 | 2 |
| #6390 | 2 |
| #451 | 7 |