Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×C7×M16 | C2 | semidirect |
| 3. #6487 | C2 | semidirect |
| 4. C2×#1132 | C2 | semidirect |
| 5. #6395 | C2 | semidirect |
| 6. #6392 | C2 | semidirect |
| 7. #6390 | C2 | semidirect |
| 37. C7×C8 | D4 | semidirect |
| 39. C2×M16 | D7 | semidirect |
| 91. C8 | C22⋊D7 | semidirect |
| 92. C7 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×M16 | 2 |
| #6493 | 2 |
| #6487 | 2 |
| C2×#1132 | 2 |
| #6395 | 2 |
| #6392 | 2 |
| #6390 | 2 |
| #468 | 7 |