Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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×#1131 | C2 | semidirect |
| 3. C2×C8×D7 | C2 | semidirect |
| 4. C7×C22⋊C8 | C2 | semidirect |
| 5. C22⋊(C7⋊C8) | C2 | semidirect |
| 6. (C2×D7)⋊C8 | C2 | semidirect |
| 7. (C2×D7)⋊C8 | C2 | semidirect |
| 51. C22⋊C8 | D7 | semidirect |
| 109. C7 | #408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157 | 2 |
| C2×#1131 | 2 |
| C2×C8×D7 | 2 |
| C7×C22⋊C8 | 2 |
| C22⋊(C7⋊C8) | 2 |
| (C2×D7)⋊C8 | 2 |
| #408 | 7 |