Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#1132 | C2 | semidirect |
| 2. C2×#1131 | C2 | semidirect |
| 3. #6460 | C2 | semidirect |
| 5. C7×#107 | C2 | semidirect |
| 6. #6384 | C2 | semidirect |
| 7. #6383 | C2 | semidirect |
| 36. C7×C8 | D4 | semidirect |
| 42. #107 | D7 | semidirect |
| 91. C8 | D28 | 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×#1132 | 2 |
| C2×#1131 | 2 |
| #6460 | 2 |
| #6458 | 2 |
| C7×#107 | 2 |
| #6384 | 2 |
| #6383 | 2 |
| #468 | 7 |