Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×C7×#41 | C2 | semidirect |
| 2. C22×D28 | C2 | semidirect |
| 3. #6512 | C2 | direct (N × H) |
| 4. C2×#1143 | C2 | semidirect |
| 5. C2×#1141 | C2 | semidirect |
| 6. C2×#1136 | C2 | semidirect |
| 9. C7×#41 | C22 | semidirect |
| 10. C2×C7×Q8 | C22 | semidirect |
| 12. C2×C7×D4 | C22 | semidirect |
| 18. C2×D28 | C22 | semidirect |
| 19. #1143 | C22 | semidirect |
| 20. #1141 | C22 | semidirect |
| 21. #1136 | C22 | semidirect |
| 22. C2×C7⋊C8 | C22 | semidirect |
| 30. C7×Q8 | C23 | semidirect |
| 33. C7×D4 | C23 | semidirect |
| 43. C7⋊C8 | C23 | semidirect |
| 44. C2×#41 | D7 | semidirect |
| 64. #41 | C2×D7 | semidirect |
| 65. C2×Q8 | C2×D7 | semidirect |
| 71. C2×D4 | C2×D7 | semidirect |
| 80. C2×C7 | AGL(1,ℤ/8) | semidirect |
| 89. Q8 | C22×D7 | semidirect |
| 95. D4 | C22×D7 | semidirect |
| 103. C7 | C2×AGL(1,ℤ/8) | semidirect |
| 119. C2 | #6512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41 | 2 |
| C22×D28 | 2 |
| #6512 | 2 |
| C2×#1143 | 2 |
| C2×#1141 | 2 |
| C2×#1136 | 2 |
| C2×AGL(1,ℤ/8) | 7 |