Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 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. D7×C4⋊C4 | C2 | semidirect |
| 4. C7×#102 | C2 | semidirect |
| 5. #6406 | C2 | semidirect |
| 6. #6395 | C2 | semidirect |
| 7. #6383 | C2 | semidirect |
| 12. D4×D7 | C4 | semidirect |
| 16. C2×C7×C8 | C22 | semidirect |
| 17. C7×C4⋊C4 | C22 | semidirect |
| 18. C4⋊Dic7 | C22 | semidirect |
| 20. C2×C7⋊C8 | C22 | semidirect |
| 30. C7×D4 | C2×C4 | semidirect |
| 37. D28 | C2×C4 | semidirect |
| 49. #102 | D7 | direct (N × H) |
| 76. C2×C8 | C2×D7 | semidirect |
| 79. C4⋊C4 | C2×D7 | semidirect |
| 85. D7 | #102 | direct (N × H) |
| 96. D4 | C4×D7 | semidirect |
| 106. C7 | C2×#102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D7 | 2 |
| C2×C8×D7 | 2 |
| D7×C4⋊C4 | 2 |
| C7×#102 | 2 |
| #6406 | 2 |
| #6395 | 2 |
| #6383 | 2 |
| C2×#102 | 7 |