Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
154 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 67 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. #6489 | C2 | semidirect |
| 3. C2×#1136 | C2 | semidirect |
| 4. #6411 | C2 | semidirect |
| 7. C7×#41 | C4 | semidirect |
| 9. C2×C7×Q8 | C4 | semidirect |
| 11. C2×C7×D4 | C4 | semidirect |
| 16. C4×Dic7 | C22 | semidirect |
| 18. #1136 | C22 | semidirect |
| 58. #41 | Dic7 | semidirect |
| 60. C2×Q8 | Dic7 | semidirect |
| 62. C2×D4 | Dic7 | 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×C7×#41 | 2 |
| #6489 | 2 |
| C2×#1136 | 2 |
| #6411 | 2 |
| #421 | 7 |