Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×C4×Dic7 | C2 | semidirect |
| 4. #6399 | C2 | direct (N × H) |
| 10. #1157 | C4 | semidirect |
| 12. C2×D28 | C4 | semidirect |
| 14. C2×Dic14 | C4 | semidirect |
| 16. C7×M16 | C22 | semidirect |
| 19. C4×Dic7 | C22 | semidirect |
| 35. D28 | C2×C4 | semidirect |
| 39. Dic14 | C2×C4 | semidirect |
| 42. C2×M16 | D7 | semidirect |
| 68. M16 | C2×D7 | semidirect |
| 74. C2×C7 | #104 | semidirect |
| 97. C7 | C2×#104 | semidirect |
| 113. C2 | #6399 | direct (N × H) |
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 |
| C2×C4×Dic7 | 2 |
| #6399 | 2 |
| C2×#104 | 7 |