Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4⋊Dic7 | C2 | semidirect |
| 3. C2×#1136 | C2 | semidirect |
| 4. #6409 | C2 | semidirect |
| 5. #6406 | C2 | semidirect |
| 7. C7×#41 | C4 | semidirect |
| 22. C7×Q8 | C2×C4 | semidirect |
| 25. C7×D4 | C2×C4 | semidirect |
| 53. #41 | Dic7 | semidirect |
| 72. Q8 | C2×Dic7 | semidirect |
| 75. D4 | C2×Dic7 | semidirect |
| 85. C7 | #417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41 | 2 |
| C2×C4⋊Dic7 | 2 |
| C2×#1136 | 2 |
| #6409 | 2 |
| #6406 | 2 |
| #417 | 7 |