Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. C2×C7×M16 | C2 | semidirect |
| 3. #6489 | C2 | semidirect |
| 4. #6399 | C2 | semidirect |
| 9. #1157 | C4 | semidirect |
| 11. C2×D28 | C4 | semidirect |
| 13. C2×Dic14 | C4 | semidirect |
| 15. C7×M16 | C22 | semidirect |
| 19. C4×Dic7 | C22 | semidirect |
| 41. C2×M16 | D7 | semidirect |
| 66. M16 | C2×D7 | semidirect |
| 95. C7 | #421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157 | 2 |
| C2×C7×M16 | 2 |
| #6489 | 2 |
| #6399 | 2 |
| #421 | 7 |