Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
202 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 73 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×C8×D7 | C2 | semidirect |
| 3. C7×C22⋊C8 | C2 | semidirect |
| 4. C22⋊(C7⋊C8) | C2 | semidirect |
| 5. (C2×D7)⋊C8 | C2 | semidirect |
| 14. C2×C7×C8 | C22 | semidirect |
| 15. C2×C7⋊C8 | C22 | semidirect |
| 21. C22×D7 | C8 | semidirect |
| 40. C22⋊C8 | D7 | direct (N × H) |
| 43. C22×C7 | C2×C8 | semidirect |
| 50. C2×D7 | C2×C8 | semidirect |
| 66. C2×C8 | C2×D7 | semidirect |
| 72. D7 | C22⋊C8 | direct (N × H) |
| 91. C7 | C2×C22⋊C8 | semidirect |
| 101. C22 | C8×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D7 | 2 |
| C2×C8×D7 | 2 |
| C7×C22⋊C8 | 2 |
| C22⋊(C7⋊C8) | 2 |
| (C2×D7)⋊C8 | 2 |
| C2×C22⋊C8 | 7 |