Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 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 |
|---|---|---|
| 4. C7×#103 | C2 | semidirect |
| 5. #6409 | C2 | semidirect |
| 6. #6390 | C2 | semidirect |
| 7. #6384 | C2 | semidirect |
| 10. Q8×D7 | C4 | semidirect |
| 25. C7×Q8 | C2×C4 | semidirect |
| 38. Dic14 | C2×C4 | semidirect |
| 47. #103 | D7 | direct (N × H) |
| 76. D7 | #103 | direct (N × H) |
| 82. Q8 | C4×D7 | semidirect |
| 95. C7 | C2×#103 | 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×C8×D7 | 2 |
| D7×C4⋊C4 | 2 |
| C7×#103 | 2 |
| #6409 | 2 |
| #6390 | 2 |
| #6384 | 2 |
| C2×#103 | 7 |