Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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. #6509 | C2 | semidirect |
| 2. C2×#1143 | C2 | semidirect |
| 3. C2×#1131 | C2 | semidirect |
| 5. C7×#103 | C2 | semidirect |
| 6. #6395 | C2 | semidirect |
| 7. #6381 | C2 | semidirect |
| 37. C7⋊C8 | D4 | semidirect |
| 43. #103 | 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 |
|---|---|
| #6509 | 2 |
| C2×#1143 | 2 |
| C2×#1131 | 2 |
| #6458 | 2 |
| C7×#103 | 2 |
| #6395 | 2 |
| #6381 | 2 |
| #468 | 7 |