Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 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×Q16 | C2 | semidirect |
| 3. Q8×Dic7 | C2 | semidirect |
| 5. #6409 | C2 | semidirect |
| 7. Dic7⋊C8 | C2 | semidirect |
| 37. C2×Q16 | D7 | semidirect |
| 87. C7 | #464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×Q16 | 2 |
| #6510 | 2 |
| Q8×Dic7 | 2 |
| C2×#1143 | 2 |
| #6409 | 2 |
| #6395 | 2 |
| Dic7⋊C8 | 2 |
| #464 | 7 |