Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 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. C4×C7×D4 | C2 | semidirect |
| 3. D4×Dic7 | C2 | semidirect |
| 4. C4×C22⋊D7 | C2 | semidirect |
| 5. C2×C4×Dic7 | C2 | semidirect |
| 6. #6455 | C2 | semidirect |
| 7. #6450 | C2 | semidirect |
| 8. (C22⋊D7)⋊C4 | C2 | semidirect |
| 9. #6440 | C2 | semidirect |
| 10. C42×D7 | C2 | semidirect |
| 11. C4×Dic14 | C2 | semidirect |
| 17. #1159 | C4 | direct (N × H) |
| 39. C7×D4 | C2×C4 | semidirect |
| 45. C22⋊D7 | C2×C4 | semidirect |
| 47. C2×Dic7 | C2×C4 | semidirect |
| 55. C4×D7 | C2×C4 | semidirect |
| 56. Dic14 | C2×C4 | semidirect |
| 63. C4×D4 | D7 | semidirect |
| 78. C4×C7 | #41 | semidirect |
| 83. Dic7 | #41 | semidirect |
| 117. D4 | C4×D7 | semidirect |
| 133. C7 | C4×#41 | semidirect |
| 149. C4 | #1159 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1159 | 2 |
| C4×C7×D4 | 2 |
| D4×Dic7 | 2 |
| C4×C22⋊D7 | 2 |
| C2×C4×Dic7 | 2 |
| #6455 | 2 |
| #6450 | 2 |
| (C22⋊D7)⋊C4 | 2 |
| #6440 | 2 |
| C42×D7 | 2 |
| C4×Dic14 | 2 |
| C4×#41 | 7 |