Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
172 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. C7×C4⋊C16 | C2 | semidirect |
| 4. Dic7⋊C16 | C2 | semidirect |
| 5. C4⋊(C7⋊C16) | C2 | semidirect |
| 37. C4⋊C16 | D7 | semidirect |
| 69. C4×C7 | M32 | semidirect |
| 74. Dic7 | M32 | semidirect |
| 111. C7 | #2150 | semidirect |
| 120. C4 | #6372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6372 | 2 |
| C4×C8×D7 | 2 |
| C7×C4⋊C16 | 2 |
| Dic7⋊C16 | 2 |
| C4⋊(C7⋊C16) | 2 |
| #2150 | 7 |