Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #6472 | C2 | semidirect |
| 3. C2×#1132 | C2 | semidirect |
| 4. #6464 | C2 | semidirect |
| 5. C7×#108 | C2 | semidirect |
| 6. #6398 | C2 | semidirect |
| 7. #6397 | C2 | semidirect |
| 44. #108 | D7 | semidirect |
| 90. C7 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6472 | 2 |
| #6471 | 2 |
| C2×#1132 | 2 |
| #6464 | 2 |
| C7×#108 | 2 |
| #6398 | 2 |
| #6397 | 2 |
| #471 | 7 |